Abstract
A novel data hiding method based on overlapped (7,4) Hamming code is proposed in this paper. 11-bit codewords are constructed from two overlapped (7,4) Hamming codes, and then a look-up table of 11-bit codeword is established, from which the suitable 11-bit codeword can be selected to minimize the stego image distortion. Because Hamming codes, rather than the bits of the pixels, are overlapped, the embedding capacity is improved remarkably. Two transferring stages are jointly optimized to minimize the stego image distortion and improve the visual quality. Several construction modes are designed and available to balance the embedding capacity and visual quality, so the modes can be selected flexibly. The systematical theoretical analysis consistent with the experimental results solidly confirms the advantages of the proposed method.
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Acknowledgements
This research was funded by the National Natural Science Foundation of China (61866028, 61866025, 61763033, 62162045), Technology Innovation Guidance Program Project (Special Project of Technology Cooperation, Science and Technology Department of Jiangxi Province) (20212BDH81003), and Open Foundation of Key Laboratory of Jiangxi Province for Image Processing and Pattern Recognition (ET201680245).
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Haoyang Kang: Methodology, Software, Validation, Investigation, Visualization, Writing - Original Draft. Lu Leng: Conceptualization, Resources, Writing - Review & Editing, Supervision. Chin-Chen Chang: Conceptualization, Supervision, Writing - Review & Editing.
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Appendix 1
Appendix 1
1st 3-bit secret | 2nd 3-bit secret | 11-bit overlapping (7,4) Hamming Code | |||||||
[0 0 0] | [0 0 0] | 00000000000 | 00000001101 | 00011010001 | 00011011100 | 00101110010 | 00101111111 | 00110100011 | 00110101110 |
01000110100 | 01000111001 | 01011100101 | 01011101000 | 01101000110 | 01101001011 | 01110010111 | 01110011010 | ||
10,001,100,101 | 10,001,101,000 | 10,010,110,100 | 10,010,111,001 | 10,100,010,111 | 10,100,011,010 | 10,111,000,110 | 10,111,001,011 | ||
11,001,010,001 | 11,001,011,100 | 11,010,000,000 | 11,010,001,101 | 11,100,100,011 | 11,100,101,110 | 11,111,110,010 | 11,111,111,111 | ||
[1 0 0] | 00000000110 | 00000001011 | 00011010111 | 00011011010 | 00101110100 | 00101111001 | 00110100101 | 00110101000 | |
01000110010 | 01000111111 | 01011100011 | 01011101110 | 01101000000 | 01101001101 | 01110010001 | 01110011100 | ||
10,001,100,011 | 10,001,101,110 | 10,010,110,010 | 10,010,111,111 | 10,100,010,001 | 10,100,011,100 | 10,111,000,000 | 10,111,001,101 | ||
11,001,010,111 | 11,001,011,010 | 11,010,000,110 | 11,010,001,011 | 11,100,100,101 | 11,100,101,000 | 11,111,110,100 | 11,111,111,001 | ||
[0 1 0] | 00000000011 | 00000001110 | 00011010010 | 00011011111 | 00101110001 | 00101111100 | 00110100000 | 00110101101 | |
01000110111 | 01000111010 | 01011100110 | 01011101011 | 01101000101 | 01101001000 | 01110010100 | 01110011001 | ||
10,001,100,110 | 10,001,101,011 | 10,010,110,111 | 10,010,111,010 | 10,100,010,100 | 10,100,011,001 | 10,111,000,101 | 10,111,001,000 | ||
11,001,010,010 | 11,001,011,111 | 11,010,000,011 | 11,010,001,110 | 11,100,100,000 | 11,100,101,101 | 11,111,110,001 | 11,111,111,100 | ||
[0 0 1] | 00000000111 | 00000001010 | 00011010110 | 00011011011 | 00101110101 | 00101111000 | 00110100100 | 00110101001 | |
01000110011 | 01000111110 | 01011100010 | 01011101111 | 01101000001 | 01101001100 | 01110010000 | 01110011101 | ||
10,001,100,010 | 10,001,101,111 | 10,010,110,011 | 10,010,111,110 | 10,100,010,000 | 10,100,011,101 | 10,111,000,001 | 10,111,001,100 | ||
11,001,010,110 | 11,001,011,011 | 11,010,000,111 | 11,010,001,010 | 11,100,100,100 | 11,100,101,001 | 11,111,110,101 | 11,111,111,000 | ||
[1 1 0] | 00000001000 | 00000000101 | 00011011001 | 00011010100 | 00101111010 | 00101110111 | 00110101011 | 00110100110 | |
01000111100 | 01000110001 | 01011101101 | 01011100000 | 01101001110 | 01101000011 | 01110011111 | 01110010010 | ||
10,001,101,101 | 10,001,100,000 | 10,010,111,100 | 10,010,110,001 | 10,100,011,111 | 10,100,010,010 | 10,111,001,110 | 10,111,000,011 | ||
11,001,011,001 | 11,001,010,100 | 11,010,001,000 | 11,010,000,101 | 11,100,101,011 | 11,100,100,110 | 11,111,111,010 | 11,111,110,111 | ||
[0 1 1] | 00000000100 | 00000001001 | 00011010101 | 00011011000 | 00101110110 | 00101111011 | 00110100111 | 00110101010 | |
01000110000 | 01000111101 | 01011100001 | 01011101100 | 01101000010 | 01101001111 | 01110010011 | 01110011110 | ||
10,001,100,001 | 10,001,101,100 | 10,010,110,000 | 10,010,111,101 | 10,100,010,011 | 10,100,011,110 | 10,111,000,010 | 10,111,001,111 | ||
11,001,010,101 | 11,001,011,000 | 11,010,000,100 | 11,010,001,001 | 11,100,100,111 | 11,100,101,010 | 11,111,110,110 | 11,111,111,011 | ||
[1 1 1] | 00000000010 | 00000001111 | 00011010011 | 00011011110 | 00101110000 | 00101111101 | 00110100001 | 00110101100 | |
01000110110 | 01000111011 | 01011100111 | 01011101010 | 01101000100 | 01101001001 | 01110010101 | 01110011000 | ||
10,001,100,111 | 10,001,101,010 | 10,010,110,110 | 10,010,111,011 | 10,100,010,101 | 10,100,011,000 | 10,111,000,100 | 10,111,001,001 | ||
11,001,010,011 | 11,001,011,110 | 11,010,000,010 | 11,010,001,111 | 11,100,100,001 | 11,100,101,100 | 11,111,110,000 | 11,111,111,101 | ||
[1 0 1] | 00000000001 | 00000001100 | 00011010000 | 00011011101 | 00101110011 | 00101111110 | 00110100010 | 00110101111 | |
01000110101 | 01000111000 | 01011100100 | 01011101001 | 01101000111 | 01101001010 | 01110010110 | 01110011011 | ||
10,001,100,100 | 10,001,101,001 | 10,010,110,101 | 10,010,111,000 | 10,100,010,110 | 10,100,011,011 | 10,111,000,111 | 10,111,001,010 | ||
11,001,010,000 | 11,001,011,101 | 11,010,000,001 | 11,010,001,100 | 11,100,100,010 | 11,100,101,111 | 11,111,110,011 | 11,111,111,110 | ||
[1 0 0] | [0 0 0] | 10,000,000,000 | 10,000,001,101 | 10,011,010,001 | 10,011,011,100 | 10,101,110,010 | 10,101,111,111 | 10,110,100,011 | 10,110,101,110 |
11,000,110,100 | 11,000,111,001 | 11,011,100,101 | 11,011,101,000 | 11,101,000,110 | 11,101,001,011 | 11,110,010,111 | 11,110,011,010 | ||
00001100101 | 00001101000 | 00010110100 | 00010111001 | 00100010111 | 00100011010 | 00111000110 | 00111001011 | ||
01001010001 | 01001011100 | 01010000000 | 01010001101 | 01100100011 | 01100101110 | 01111110010 | 01111111111 | ||
[1 0 0] | 10,000,000,110 | 10,000,001,011 | 10,011,010,111 | 10,011,011,010 | 10,101,110,100 | 10,101,111,001 | 10,110,100,101 | 10,110,101,000 | |
11,000,110,010 | 11,000,111,111 | 11,011,100,011 | 11,011,101,110 | 11,101,000,000 | 11,101,001,101 | 11,110,010,001 | 11,110,011,100 | ||
00001100011 | 00001101110 | 00010110010 | 00010111111 | 00100010001 | 00100011100 | 00111000000 | 00111001101 | ||
01001010111 | 01001011010 | 01010000110 | 01010001011 | 01100100101 | 01100101000 | 01111110100 | 01111111001 | ||
[0 1 0] | 10,000,000,011 | 10,000,001,110 | 10,011,010,010 | 10,011,011,111 | 10,101,110,001 | 10,101,111,100 | 10,110,100,000 | 10,110,101,101 | |
11,000,110,111 | 11,000,111,010 | 11,011,100,110 | 11,011,101,011 | 11,101,000,101 | 11,101,001,000 | 11,110,010,100 | 11,110,011,001 | ||
00001100110 | 00001101011 | 00010110111 | 00010111010 | 00100010100 | 00100011001 | 00111000101 | 00111001000 | ||
01001010010 | 01001011111 | 01010000011 | 01010001110 | 01100100000 | 01100101101 | 01111110001 | 01111111100 | ||
[0 0 1] | 10,000,000,111 | 10,000,001,010 | 10,011,010,110 | 10,011,011,011 | 10,101,110,101 | 10,101,111,000 | 10,110,100,100 | 10,110,101,001 | |
11,000,110,011 | 11,000,111,110 | 11,011,100,010 | 11,011,101,111 | 11,101,000,001 | 11,101,001,100 | 11,110,010,000 | 11,110,011,101 | ||
00001100010 | 00001101111 | 00010110011 | 00010111110 | 00100010000 | 00100011101 | 00111000001 | 00111001100 | ||
01001010110 | 01001011011 | 01010000111 | 01010001010 | 01100100100 | 01100101001 | 01111110101 | 01111111000 | ||
[1 1 0] | 10,000,001,000 | 10,000,000,101 | 10,011,011,001 | 10,011,010,100 | 10,101,111,010 | 10,101,110,111 | 10,110,101,011 | 10,110,100,110 | |
11,000,111,100 | 11,000,110,001 | 11,011,101,101 | 11,011,100,000 | 11,101,001,110 | 11,101,000,011 | 11,110,011,111 | 11,110,010,010 | ||
00001101101 | 00001100000 | 00010111100 | 00010110001 | 00100011111 | 00100010010 | 00111001110 | 00111000011 | ||
01001011001 | 01001010100 | 01010001000 | 01010000101 | 01100101011 | 01100100110 | 01111111010 | 01111110111 | ||
[0 1 1] | 10,000,000,100 | 10,000,001,001 | 10,011,010,101 | 10,011,011,000 | 10,101,110,110 | 10,101,111,011 | 10,110,100,111 | 10,110,101,010 | |
11,000,110,000 | 11,000,111,101 | 11,011,100,001 | 11,011,101,100 | 11,101,000,010 | 11,101,001,111 | 11,110,010,011 | 11,110,011,110 | ||
00001100001 | 00001101100 | 00010110000 | 00010111101 | 00100010011 | 00100011110 | 00111000010 | 00111001111 | ||
01001010101 | 01001011000 | 01010000100 | 01010001001 | 01100100111 | 01100101010 | 01111110110 | 01111111011 | ||
[1 1 1] | 10,000,000,010 | 10,000,001,111 | 10,011,010,011 | 10,011,011,110 | 10,101,110,000 | 10,101,111,101 | 10,110,100,001 | 10,110,101,100 | |
11,000,110,110 | 11,000,111,011 | 11,011,100,111 | 11,011,101,010 | 11,101,000,100 | 11,101,001,001 | 11,110,010,101 | 11,110,011,000 | ||
00001100111 | 00001101010 | 00010110110 | 00010111011 | 00100010101 | 00100011000 | 00111000100 | 00111001001 | ||
01001010011 | 01001011110 | 01010000010 | 01010001111 | 01100100001 | 01100101100 | 01111110000 | 01111111101 | ||
[1 0 1] | 10,000,000,001 | 10,000,001,100 | 10,011,010,000 | 10,011,011,101 | 10,101,110,011 | 10,101,111,110 | 10,110,100,010 | 10,110,101,111 | |
11,000,110,101 | 11,000,111,000 | 11,011,100,100 | 11,011,101,001 | 11,101,000,111 | 11,101,001,010 | 11,110,010,110 | 11,110,011,011 | ||
00001100100 | 00001101001 | 00010110101 | 00010111000 | 00100010110 | 00100011011 | 00111000111 | 00111001010 | ||
01001010000 | 01001011101 | 01010000001 | 01010001100 | 01100100010 | 01100101111 | 01111110011 | 01111111110 | ||
[0 1 0] | [0 0 0] | 01000000000 | 01000001101 | 01011010001 | 01011011100 | 01101110010 | 01101111111 | 01110100011 | 01110101110 |
00000110100 | 00000111001 | 00011100101 | 00011101000 | 00101000110 | 00101001011 | 00110010111 | 00110011010 | ||
11,001,100,101 | 11,001,101,000 | 11,010,110,100 | 11,010,111,001 | 11,100,010,111 | 11,100,011,010 | 11,111,000,110 | 11,111,001,011 | ||
10,001,010,001 | 10,001,011,100 | 10,010,000,000 | 10,010,001,101 | 10,100,100,011 | 10,100,101,110 | 10,111,110,010 | 10,111,111,111 | ||
[1 0 0] | 01000000110 | 01000001011 | 01011010111 | 01011011010 | 01101110100 | 01101111001 | 01110100101 | 01110101000 | |
00000110010 | 00000111111 | 00011100011 | 00011101110 | 00101000000 | 00101001101 | 00110010001 | 00110011100 | ||
11,001,100,011 | 11,001,101,110 | 11,010,110,010 | 11,010,111,111 | 11,100,010,001 | 11,100,011,100 | 11,111,000,000 | 11,111,001,101 | ||
10,001,010,111 | 10,001,011,010 | 10,010,000,110 | 10,010,001,011 | 10,100,100,101 | 10,100,101,000 | 10,111,110,100 | 10,111,111,001 | ||
[0 1 0] | 01000000011 | 01000001110 | 01011010010 | 01011011111 | 01101110001 | 01101111100 | 01110100000 | 01110101101 | |
00000110111 | 00000111010 | 00011100110 | 00011101011 | 00101000101 | 00101001000 | 00110010100 | 00110011001 | ||
11,001,100,110 | 11,001,101,011 | 11,010,110,111 | 11,010,111,010 | 11,100,010,100 | 11,100,011,001 | 11,111,000,101 | 11,111,001,000 | ||
10,001,010,010 | 10,001,011,111 | 10,010,000,011 | 10,010,001,110 | 10,100,100,000 | 10,100,101,101 | 10,111,110,001 | 10,111,111,100 | ||
[0 0 1] | 01000000111 | 01000001010 | 01011010110 | 01011011011 | 01101110101 | 01101111000 | 01110100100 | 01110101001 | |
00000110011 | 00000111110 | 00011100010 | 00011101111 | 00101000001 | 00101001100 | 00110010000 | 00110011101 | ||
11,001,100,010 | 11,001,101,111 | 11,010,110,011 | 11,010,111,110 | 11,100,010,000 | 11,100,011,101 | 11,111,000,001 | 11,111,001,100 | ||
10,001,010,110 | 10,001,011,011 | 10,010,000,111 | 10,010,001,010 | 10,100,100,100 | 10,100,101,001 | 10,111,110,101 | 10,111,111,000 | ||
[1 1 0] | 01000001000 | 01000000101 | 01011011001 | 01011010100 | 01101111010 | 01101110111 | 01110101011 | 01110100110 | |
00000111100 | 00000110001 | 00011101101 | 00011100000 | 00101001110 | 00101000011 | 00110011111 | 00110010010 | ||
11,001,101,101 | 11,001,100,000 | 11,010,111,100 | 11,010,110,001 | 11,100,011,111 | 11,100,010,010 | 11,111,001,110 | 11,111,000,011 | ||
10,001,011,001 | 10,001,010,100 | 10,010,001,000 | 10,010,000,101 | 10,100,101,011 | 10,100,100,110 | 10,111,111,010 | 10,111,110,111 | ||
[0 1 1] | 01000000100 | 01000001001 | 01011010101 | 01011011000 | 01101110110 | 01101111011 | 01110100111 | 01110101010 | |
00000110000 | 00000111101 | 00011100001 | 00011101100 | 00101000010 | 00101001111 | 00110010011 | 00110011110 | ||
11,001,100,001 | 11,001,101,100 | 11,010,110,000 | 11,010,111,101 | 11,100,010,011 | 11,100,011,110 | 11,111,000,010 | 11,111,001,111 | ||
10,001,010,101 | 10,001,011,000 | 10,010,000,100 | 10,010,001,001 | 10,100,100,111 | 10,100,101,010 | 10,111,110,110 | 10,111,111,011 | ||
[1 1 1] | 01000000010 | 01000001111 | 01011010011 | 01011011110 | 01101110000 | 01101111101 | 01110100001 | 01110101100 | |
00000110110 | 00000111011 | 00011100111 | 00011101010 | 00101000100 | 00101001001 | 00110010101 | 00110011000 | ||
11,001,100,111 | 11,001,101,010 | 11,010,110,110 | 11,010,111,011 | 11,100,010,101 | 11,100,011,000 | 11,111,000,100 | 11,111,001,001 | ||
10,001,010,011 | 10,001,011,110 | 10,010,000,010 | 10,010,001,111 | 10,100,100,001 | 10,100,101,100 | 10,111,110,000 | 10,111,111,101 | ||
[1 0 1] | 01000000001 | 01000001100 | 01011010000 | 01011011101 | 01101110011 | 01101111110 | 01110100010 | 01110101111 | |
00000110101 | 00000111000 | 00011100100 | 00011101001 | 00101000111 | 00101001010 | 00110010110 | 00110011011 | ||
11,001,100,100 | 11,001,101,001 | 11,010,110,101 | 11,010,111,000 | 11,100,010,110 | 11,100,011,011 | 11,111,000,111 | 11,111,001,010 | ||
10,001,010,000 | 10,001,011,101 | 10,010,000,001 | 10,010,001,100 | 10,100,100,010 | 10,100,101,111 | 10,111,110,011 | 10,111,111,110 | ||
[0 0 1] | [0 0 0] | 00100000000 | 00100001101 | 00111010001 | 00111011100 | 00001110010 | 00001111111 | 00010100011 | 00010101110 |
01100110100 | 01100111001 | 01111100101 | 01111101000 | 01001000110 | 01001001011 | 01010010111 | 01010011010 | ||
10,101,100,101 | 10,101,101,000 | 10,110,110,100 | 10,110,111,001 | 10,000,010,111 | 10,000,011,010 | 10,011,000,110 | 10,011,001,011 | ||
11,101,010,001 | 11,101,011,100 | 11,110,000,000 | 11,110,001,101 | 11,000,100,011 | 11,000,101,110 | 11,011,110,010 | 11,011,111,111 | ||
[1 0 0] | 00100000110 | 00100001011 | 00111010111 | 00111011010 | 00001110100 | 00001111001 | 00010100101 | 00010101000 | |
01100110010 | 01100111111 | 01111100011 | 01111101110 | 01001000000 | 01001001101 | 01010010001 | 01010011100 | ||
10,101,100,011 | 10,101,101,110 | 10,110,110,010 | 10,110,111,111 | 10,000,010,001 | 10,000,011,100 | 10,011,000,000 | 10,011,001,101 | ||
11,101,010,111 | 11,101,011,010 | 11,110,000,110 | 11,110,001,011 | 11,000,100,101 | 11,000,101,000 | 11,011,110,100 | 11,011,111,001 | ||
[0 1 0] | 00100000011 | 00100001110 | 00111010010 | 00111011111 | 00001110001 | 00001111100 | 00010100000 | 00010101101 | |
01100110111 | 01100111010 | 01111100110 | 01111101011 | 01001000101 | 01001001000 | 01010010100 | 01010011001 | ||
10,101,100,110 | 10,101,101,011 | 10,110,110,111 | 10,110,111,010 | 10,000,010,100 | 10,000,011,001 | 10,011,000,101 | 10,011,001,000 | ||
11,101,010,010 | 11,101,011,111 | 11,110,000,011 | 11,110,001,110 | 11,000,100,000 | 11,000,101,101 | 11,011,110,001 | 11,011,111,100 | ||
[0 0 1] | 00100000111 | 00100001010 | 00111010110 | 00111011011 | 00001110101 | 00001111000 | 00010100100 | 00010101001 | |
01100110011 | 01100111110 | 01111100010 | 01111101111 | 01001000001 | 01001001100 | 01010010000 | 01010011101 | ||
10,101,100,010 | 10,101,101,111 | 10,110,110,011 | 10,110,111,110 | 10,000,010,000 | 10,000,011,101 | 10,011,000,001 | 10,011,001,100 | ||
11,101,010,110 | 11,101,011,011 | 11,110,000,111 | 11,110,001,010 | 11,000,100,100 | 11,000,101,001 | 11,011,110,101 | 11,011,111,000 | ||
[1 1 0] | 00100001000 | 00100000101 | 00111011001 | 00111010100 | 00001111010 | 00001110111 | 00010101011 | 00010100110 | |
01100111100 | 01100110001 | 01111101101 | 01111100000 | 01001001110 | 01001000011 | 01010011111 | 01010010010 | ||
10,101,101,101 | 10,101,100,000 | 10,110,111,100 | 10,110,110,001 | 10,000,011,111 | 10,000,010,010 | 10,011,001,110 | 10,011,000,011 | ||
11,101,011,001 | 11,101,010,100 | 11,110,001,000 | 11,110,000,101 | 11,000,101,011 | 11,000,100,110 | 11,011,111,010 | 11,011,110,111 | ||
[0 1 1] | 00100000100 | 00100001001 | 00111010101 | 00111011000 | 00001110110 | 00001111011 | 00010100111 | 00010101010 | |
01100110000 | 01100111101 | 01111100001 | 01111101100 | 01001000010 | 01001001111 | 01010010011 | 01010011110 | ||
10,101,100,001 | 10,101,101,100 | 10,110,110,000 | 10,110,111,101 | 10,000,010,011 | 10,000,011,110 | 10,011,000,010 | 10,011,001,111 | ||
11,101,010,101 | 11,101,011,000 | 11,110,000,100 | 11,110,001,001 | 11,000,100,111 | 11,000,101,010 | 11,011,110,110 | 11,011,111,011 | ||
[1 1 1] | 00100000010 | 00100001111 | 00111010011 | 00111011110 | 00001110000 | 00001111101 | 00010100001 | 00010101100 | |
01100110110 | 01100111011 | 01111100111 | 01111101010 | 01001000100 | 01001001001 | 01010010101 | 01010011000 | ||
10,101,100,111 | 10,101,101,010 | 10,110,110,110 | 10,110,111,011 | 10,000,010,101 | 10,000,011,000 | 10,011,000,100 | 10,011,001,001 | ||
11,101,010,011 | 11,101,011,110 | 11,110,000,010 | 11,110,001,111 | 11,000,100,001 | 11,000,101,100 | 11,011,110,000 | 11,011,111,101 | ||
[1 0 1] | 00100000001 | 00100001100 | 00111010000 | 00111011101 | 00001110011 | 00001111110 | 00010100010 | 00010101111 | |
01100110101 | 01100111000 | 01111100100 | 01111101001 | 01001000111 | 01001001010 | 01010010110 | 01010011011 | ||
10,101,100,100 | 10,101,101,001 | 10,110,110,101 | 10,110,111,000 | 10,000,010,110 | 10,000,011,011 | 10,011,000,111 | 10,011,001,010 | ||
11,101,010,000 | 11,101,011,101 | 11,110,000,001 | 11,110,001,100 | 11,000,100,010 | 11,000,101,111 | 11,011,110,011 | 11,011,111,110 | ||
[1 1 0] | [0 0 0] | 00010000000 | 00010001101 | 00001010001 | 00001011100 | 00111110010 | 00111111111 | 00100100011 | 00100101110 |
01010110100 | 01010111001 | 01001100101 | 01001101000 | 01111000110 | 01111001011 | 01100010111 | 01100011010 | ||
10,011,100,101 | 10,011,101,000 | 10,000,110,100 | 10,000,111,001 | 10,110,010,111 | 10,110,011,010 | 10,101,000,110 | 10,101,001,011 | ||
11,011,010,001 | 11,011,011,100 | 11,000,000,000 | 11,000,001,101 | 11,110,100,011 | 11,110,101,110 | 11,101,110,010 | 11,101,111,111 | ||
[1 0 0] | 00010000110 | 00010001011 | 00001010111 | 00001011010 | 00111110100 | 00111111001 | 00100100101 | 00100101000 | |
01010110010 | 01010111111 | 01001100011 | 01001101110 | 01111000000 | 01111001101 | 01100010001 | 01100011100 | ||
10,011,100,011 | 10,011,101,110 | 10,000,110,010 | 10,000,111,111 | 10,110,010,001 | 10,110,011,100 | 10,101,000,000 | 10,101,001,101 | ||
11,011,010,111 | 11,011,011,010 | 11,000,000,110 | 11,000,001,011 | 11,110,100,101 | 11,110,101,000 | 11,101,110,100 | 11,101,111,001 | ||
[0 1 0] | 00010000011 | 00010001110 | 00001010010 | 00001011111 | 00111110001 | 00111111100 | 00100100000 | 00100101101 | |
01010110111 | 01010111010 | 01001100110 | 01001101011 | 01111000101 | 01111001000 | 01100010100 | 01100011001 | ||
10,011,100,110 | 10,011,101,011 | 10,000,110,111 | 10,000,111,010 | 10,110,010,100 | 10,110,011,001 | 10,101,000,101 | 10,101,001,000 | ||
11,011,010,010 | 11,011,011,111 | 11,000,000,011 | 11,000,001,110 | 11,110,100,000 | 11,110,101,101 | 11,101,110,001 | 11,101,111,100 | ||
[0 0 1] | 00010000111 | 00010001010 | 00001010110 | 00001011011 | 00111110101 | 00111111000 | 00100100100 | 00100101001 | |
01010110011 | 01010111110 | 01001100010 | 01001101111 | 01111000001 | 01111001100 | 01100010000 | 01100011101 | ||
10,011,100,010 | 10,011,101,111 | 10,000,110,011 | 10,000,111,110 | 10,110,010,000 | 10,110,011,101 | 10,101,000,001 | 10,101,001,100 | ||
11,011,010,110 | 11,011,011,011 | 11,000,000,111 | 11,000,001,010 | 11,110,100,100 | 11,110,101,001 | 11,101,110,101 | 11,101,111,000 | ||
[1 1 0] | 00010001000 | 00010000101 | 00001011001 | 00001010100 | 00111111010 | 00111110111 | 00100101011 | 00100100110 | |
01010111100 | 01010110001 | 01001101101 | 01001100000 | 01111001110 | 01111000011 | 01100011111 | 01100010010 | ||
10,011,101,101 | 10,011,100,000 | 10,000,111,100 | 10,000,110,001 | 10,110,011,111 | 10,110,010,010 | 10,101,001,110 | 10,101,000,011 | ||
11,011,011,001 | 11,011,010,100 | 11,000,001,000 | 11,000,000,101 | 11,110,101,011 | 11,110,100,110 | 11,101,111,010 | 11,101,110,111 | ||
[0 1 1] | 00010000100 | 00010001001 | 00001010101 | 00001011000 | 00111110110 | 00111111011 | 00100100111 | 00100101010 | |
01010110000 | 01010111101 | 01001100001 | 01001101100 | 01111000010 | 01111001111 | 01100010011 | 01100011110 | ||
10,011,100,001 | 10,011,101,100 | 10,000,110,000 | 10,000,111,101 | 10,110,010,011 | 10,110,011,110 | 10,101,000,010 | 10,101,001,111 | ||
11,011,010,101 | 11,011,011,000 | 11,000,000,100 | 11,000,001,001 | 11,110,100,111 | 11,110,101,010 | 11,101,110,110 | 11,101,111,011 | ||
[1 1 1] | 00010000010 | 00010001111 | 00001010011 | 00001011110 | 00111110000 | 00111111101 | 00100100001 | 00100101100 | |
01010110110 | 01010111011 | 01001100111 | 01001101010 | 01111000100 | 01111001001 | 01100010101 | 01100011000 | ||
10,011,100,111 | 10,011,101,010 | 10,000,110,110 | 10,000,111,011 | 10,110,010,101 | 10,110,011,000 | 10,101,000,100 | 10,101,001,001 | ||
11,011,010,011 | 11,011,011,110 | 11,000,000,010 | 11,000,001,111 | 11,110,100,001 | 11,110,101,100 | 11,101,110,000 | 11,101,111,101 | ||
[1 0 1] | 00010000001 | 00010001100 | 00001010000 | 00001011101 | 00111110011 | 00111111110 | 00100100010 | 00100101111 | |
01010110101 | 01010111000 | 01001100100 | 01001101001 | 01111000111 | 01111001010 | 01100010110 | 01100011011 | ||
10,011,100,100 | 10,011,101,001 | 10,000,110,101 | 10,000,111,000 | 10,110,010,110 | 10,110,011,011 | 10,101,000,111 | 10,101,001,010 | ||
11,011,010,000 | 11,011,011,101 | 11,000,000,001 | 11,000,001,100 | 11,110,100,010 | 11,110,101,111 | 11,101,110,011 | 11,101,111,110 | ||
[0 1 1] | [0 0 0] | 00001000110 | 00001001011 | 00010010111 | 00010011010 | 00100110100 | 00100111001 | 00111100101 | 00111101000 |
01001110010 | 01001111111 | 01010100011 | 01010101110 | 01100000000 | 01100001101 | 01111010001 | 01111011100 | ||
10,000,100,011 | 10,000,101,110 | 10,011,110,010 | 10,011,111,111 | 10,101,010,001 | 10,101,011,100 | 10,110,000,000 | 10,110,001,101 | ||
11,000,010,111 | 11,000,011,010 | 11,011,000,110 | 11,011,001,011 | 11,101,100,101 | 11,101,101,000 | 11,110,110,100 | 11,110,111,001 | ||
[1 0 0] | 00001000000 | 00001001101 | 00010010001 | 00010011100 | 00100110010 | 00100111111 | 00111100011 | 00111101110 | |
01001110100 | 01001111001 | 01010100101 | 01010101000 | 01100000110 | 01100001011 | 01111010111 | 01111011010 | ||
10,000,100,101 | 10,000,101,000 | 10,011,110,100 | 10,011,111,001 | 10,101,010,111 | 10,101,011,010 | 10,110,000,110 | 10,110,001,011 | ||
11,000,010,001 | 11,000,011,100 | 11,011,000,000 | 11,011,001,101 | 11,101,100,011 | 11,101,101,110 | 11,110,110,010 | 11,110,111,111 | ||
[0 1 0] | 00001000101 | 00001001000 | 00010010100 | 00010011001 | 00100110111 | 00100111010 | 00111100110 | 00111101011 | |
01001110001 | 01001111100 | 01010100000 | 01010101101 | 01100000011 | 01100001110 | 01111010010 | 01111011111 | ||
10,000,100,000 | 10,000,101,101 | 10,011,110,001 | 10,011,111,100 | 10,101,010,010 | 10,101,011,111 | 10,110,000,011 | 10,110,001,110 | ||
11,000,010,100 | 11,000,011,001 | 11,011,000,101 | 11,011,001,000 | 11,101,100,110 | 11,101,101,011 | 11,110,110,111 | 11,110,111,010 | ||
[0 0 1] | 00001000001 | 00001001100 | 00010010000 | 00010011101 | 00100110011 | 00100111110 | 00111100010 | 00111101111 | |
01001110101 | 01001111000 | 01010100100 | 01010101001 | 01100000111 | 01100001010 | 01111010110 | 01111011011 | ||
10,000,100,100 | 10,000,101,001 | 10,011,110,101 | 10,011,111,000 | 10,101,010,110 | 10,101,011,011 | 10,110,000,111 | 10,110,001,010 | ||
11,000,010,000 | 11,000,011,101 | 11,011,000,001 | 11,011,001,100 | 11,101,100,010 | 11,101,101,111 | 11,110,110,011 | 11,110,111,110 | ||
[1 1 0] | 00001001110 | 00001000011 | 00010011111 | 00010010010 | 00100111100 | 00100110001 | 00111101101 | 00111100000 | |
01001111010 | 01001110111 | 01010101011 | 01010100110 | 01100001000 | 01100000101 | 01111011001 | 01111010100 | ||
10,000,101,011 | 10,000,100,110 | 10,011,111,010 | 10,011,110,111 | 10,101,011,001 | 10,101,010,100 | 10,110,001,000 | 10,110,000,101 | ||
11,000,011,111 | 11,000,010,010 | 11,011,001,110 | 11,011,000,011 | 11,101,101,101 | 11,101,100,000 | 11,110,111,100 | 11,110,110,001 | ||
[0 1 1] | 00001000010 | 00001001111 | 00010010011 | 00010011110 | 00100110000 | 00100111101 | 00111100001 | 00111101100 | |
01001110110 | 01001111011 | 01010100111 | 01010101010 | 01100000100 | 01100001001 | 01111010101 | 01111011000 | ||
10,000,100,111 | 10,000,101,010 | 10,011,110,110 | 10,011,111,011 | 10,101,010,101 | 10,101,011,000 | 10,110,000,100 | 10,110,001,001 | ||
11,000,010,011 | 11,000,011,110 | 11,011,000,010 | 11,011,001,111 | 11,101,100,001 | 11,101,101,100 | 11,110,110,000 | 11,110,111,101 | ||
[1 1 1] | 00001000100 | 00001001001 | 00010010101 | 00010011000 | 00100110110 | 00100111011 | 00111100111 | 00111101010 | |
01001110000 | 01001111101 | 01010100001 | 01010101100 | 01100000010 | 01100001111 | 01111010011 | 01111011110 | ||
10,000,100,001 | 10,000,101,100 | 10,011,110,000 | 10,011,111,101 | 10,101,010,011 | 10,101,011,110 | 10,110,000,010 | 10,110,001,111 | ||
11,000,010,101 | 11,000,011,000 | 11,011,000,100 | 11,011,001,001 | 11,101,100,111 | 11,101,101,010 | 11,110,110,110 | 11,110,111,011 | ||
[1 0 1] | 00001000111 | 00001001010 | 00010010110 | 00010011011 | 00100110101 | 00100111000 | 00111100100 | 00111101001 | |
01001110011 | 01001111110 | 01010100010 | 01010101111 | 01100000001 | 01100001100 | 01111010000 | 01111011101 | ||
10,000,100,010 | 10,000,101,111 | 10,011,110,011 | 10,011,111,110 | 10,101,010,000 | 10,101,011,101 | 10,110,000,001 | 10,110,001,100 | ||
11,000,010,110 | 11,000,011,011 | 11,011,000,111 | 11,011,001,010 | 11,101,100,100 | 11,101,101,001 | 11,110,110,101 | 11,110,111,000 | ||
[1 1 1] | [0 0 0] | 00000100011 | 00000101110 | 00011110010 | 00011111111 | 00101010001 | 00101011100 | 00110000000 | 00110001101 |
01000010111 | 01000011010 | 01011000110 | 01011001011 | 01101100101 | 01101101000 | 01110110100 | 01110111001 | ||
10,001,000,110 | 10,001,001,011 | 10,010,010,111 | 10,010,011,010 | 10,100,110,100 | 10,100,111,001 | 10,111,100,101 | 10,111,101,000 | ||
11,001,110,010 | 11,001,111,111 | 11,010,100,011 | 11,010,101,110 | 11,100,000,000 | 11,100,001,101 | 11,111,010,001 | 11,111,011,100 | ||
[1 0 0] | 00000100101 | 00000101000 | 00011110100 | 00011111001 | 00101010111 | 00101011010 | 00110000110 | 00110001011 | |
01000010001 | 01000011100 | 01011000000 | 01011001101 | 01101100011 | 01101101110 | 01110110010 | 01110111111 | ||
10,001,000,000 | 10,001,001,101 | 10,010,010,001 | 10,010,011,100 | 10,100,110,010 | 10,100,111,111 | 10,111,100,011 | 10,111,101,110 | ||
11,001,110,100 | 11,001,111,001 | 11,010,100,101 | 11,010,101,000 | 11,100,000,110 | 11,100,001,011 | 11,111,010,111 | 11,111,011,010 | ||
[0 1 0] | 00000100000 | 00000101101 | 00011110001 | 00011111100 | 00101010010 | 00101011111 | 00110000011 | 00110001110 | |
01000010100 | 01000011001 | 01011000101 | 01011001000 | 01101100110 | 01101101011 | 01110110111 | 01110111010 | ||
10,001,000,101 | 10,001,001,000 | 10,010,010,100 | 10,010,011,001 | 10,100,110,111 | 10,100,111,010 | 10,111,100,110 | 10,111,101,011 | ||
11,001,110,001 | 11,001,111,100 | 11,010,100,000 | 11,010,101,101 | 11,100,000,011 | 11,100,001,110 | 11,111,010,010 | 11,111,011,111 | ||
[0 0 1] | 00000100100 | 00000101001 | 00011110101 | 00011111000 | 00101010110 | 00101011011 | 00110000111 | 00110001010 | |
01000010000 | 01000011101 | 01011000001 | 01011001100 | 01101100010 | 01101101111 | 01110110011 | 01110111110 | ||
10,001,000,001 | 10,001,001,100 | 10,010,010,000 | 10,010,011,101 | 10,100,110,011 | 10,100,111,110 | 10,111,100,010 | 10,111,101,111 | ||
11,001,110,101 | 11,001,111,000 | 11,010,100,100 | 11,010,101,001 | 11,100,000,111 | 11,100,001,010 | 11,111,010,110 | 11,111,011,011 | ||
[1 1 0] | 00000101011 | 00000100110 | 00011111010 | 00011110111 | 00101011001 | 00101010100 | 00110001000 | 00110000101 | |
01000011111 | 01000010010 | 01011001110 | 01011000011 | 01101101101 | 01101100000 | 01110111100 | 01110110001 | ||
10,001,001,110 | 10,001,000,011 | 10,010,011,111 | 10,010,010,010 | 10,100,111,100 | 10,100,110,001 | 10,111,101,101 | 10,111,100,000 | ||
11,001,111,010 | 11,001,110,111 | 11,010,101,011 | 11,010,100,110 | 11,100,001,000 | 11,100,000,101 | 11,111,011,001 | 11,111,010,100 | ||
[0 1 1] | 00000100111 | 00000101010 | 00011110110 | 00011111011 | 00101010101 | 00101011000 | 00110000100 | 00110001001 | |
01000010011 | 01000011110 | 01011000010 | 01011001111 | 01101100001 | 01101101100 | 01110110000 | 01110111101 | ||
10,001,000,010 | 10,001,001,111 | 10,010,010,011 | 10,010,011,110 | 10,100,110,000 | 10,100,111,101 | 10,111,100,001 | 10,111,101,100 | ||
11,001,110,110 | 11,001,111,011 | 11,010,100,111 | 11,010,101,010 | 11,100,000,100 | 11,100,001,001 | 11,111,010,101 | 11,111,011,000 | ||
[1 1 1] | 00000100001 | 00000101100 | 00011110000 | 00011111101 | 00101010011 | 00101011110 | 00110000010 | 00110001111 | |
01000010101 | 01000011000 | 01011000100 | 01011001001 | 01101100111 | 01101101010 | 01110110110 | 01110111011 | ||
10,001,000,100 | 10,001,001,001 | 10,010,010,101 | 10,010,011,000 | 10,100,110,110 | 10,100,111,011 | 10,111,100,111 | 10,111,101,010 | ||
11,001,110,000 | 11,001,111,101 | 11,010,100,001 | 11,010,101,100 | 11,100,000,010 | 11,100,001,111 | 11,111,010,011 | 11,111,011,110 | ||
[1 0 1] | 00000100010 | 00000101111 | 00011110011 | 00011111110 | 00101010000 | 00101011101 | 00110000001 | 00110001100 | |
01000010110 | 01000011011 | 01011000111 | 01011001010 | 01101100100 | 01101101001 | 01110110101 | 01110111000 | ||
10,001,000,111 | 10,001,001,010 | 10,010,010,110 | 10,010,011,011 | 10,100,110,101 | 10,100,111,000 | 10,111,100,100 | 10,111,101,001 | ||
11,001,110,011 | 11,001,111,110 | 11,010,100,010 | 11,010,101,111 | 11,100,000,001 | 11,100,001,100 | 11,111,010,000 | 11,111,011,101 | ||
[1 0 1] | [0 0 0] | 00000010111 | 00000011010 | 00011000110 | 00011001011 | 00101100101 | 00101101000 | 00110110100 | 00110111001 |
01000100011 | 01000101110 | 01011110010 | 01011111111 | 01101010001 | 01101011100 | 01110000000 | 01110001101 | ||
10,001,110,010 | 10,001,111,111 | 10,010,100,011 | 10,010,101,110 | 10,100,000,000 | 10,100,001,101 | 10,111,010,001 | 10,111,011,100 | ||
11,001,000,110 | 11,001,001,011 | 11,010,010,111 | 11,010,011,010 | 11,100,110,100 | 11,100,111,001 | 11,111,100,101 | 11,111,101,000 | ||
[1 0 0] | 00000010001 | 00000011100 | 00011000000 | 00011001101 | 00101100011 | 00101101110 | 00110110010 | 00110111111 | |
01000100101 | 01000101000 | 01011110100 | 01011111001 | 01101010111 | 01101011010 | 01110000110 | 01110001011 | ||
10,001,110,100 | 10,001,111,001 | 10,010,100,101 | 10,010,101,000 | 10,100,000,110 | 10,100,001,011 | 10,111,010,111 | 10,111,011,010 | ||
11,001,000,000 | 11,001,001,101 | 11,010,010,001 | 11,010,011,100 | 11,100,110,010 | 11,100,111,111 | 11,111,100,011 | 11,111,101,110 | ||
[0 1 0] | 00000010100 | 00000011001 | 00011000101 | 00011001000 | 00101100110 | 00101101011 | 00110110111 | 00110111010 | |
01000100000 | 01000101101 | 01011110001 | 01011111100 | 01101010010 | 01101011111 | 01110000011 | 01110001110 | ||
10,001,110,001 | 10,001,111,100 | 10,010,100,000 | 10,010,101,101 | 10,100,000,011 | 10,100,001,110 | 10,111,010,010 | 10,111,011,111 | ||
11,001,000,101 | 11,001,001,000 | 11,010,010,100 | 11,010,011,001 | 11,100,110,111 | 11,100,111,010 | 11,111,100,110 | 11,111,101,011 | ||
[0 0 1] | 00000010000 | 00000011101 | 00011000001 | 00011001100 | 00101100010 | 00101101111 | 00110110011 | 00110111110 | |
01000100100 | 01000101001 | 01011110101 | 01011111000 | 01101010110 | 01101011011 | 01110000111 | 01110001010 | ||
10,001,110,101 | 10,001,111,000 | 10,010,100,100 | 10,010,101,001 | 10,100,000,111 | 10,100,001,010 | 10,111,010,110 | 10,111,011,011 | ||
11,001,000,001 | 11,001,001,100 | 11,010,010,000 | 11,010,011,101 | 11,100,110,011 | 11,100,111,110 | 11,111,100,010 | 11,111,101,111 | ||
[1 1 0] | 00000011111 | 00000010010 | 00011001110 | 00011000011 | 00101101101 | 00101100000 | 00110111100 | 00110110001 | |
01000101011 | 01000100110 | 01011111010 | 01011110111 | 01101011001 | 01101010100 | 01110001000 | 01110000101 | ||
10,001,111,010 | 10,001,110,111 | 10,010,101,011 | 10,010,100,110 | 10,100,001,000 | 10,100,000,101 | 10,111,011,001 | 10,111,010,100 | ||
11,001,001,110 | 11,001,000,011 | 11,010,011,111 | 11,010,010,010 | 11,100,111,100 | 11,100,110,001 | 11,111,101,101 | 11,111,100,000 | ||
[0 1 1] | 00000010011 | 00000011110 | 00011000010 | 00011001111 | 00101100001 | 00101101100 | 00110110000 | 00110111101 | |
01000100111 | 01000101010 | 01011110110 | 01011111011 | 01101010101 | 01101011000 | 01110000100 | 01110001001 | ||
10,001,110,110 | 10,001,111,011 | 10,010,100,111 | 10,010,101,010 | 10,100,000,100 | 10,100,001,001 | 10,111,010,101 | 10,111,011,000 | ||
11,001,000,010 | 11,001,001,111 | 11,010,010,011 | 11,010,011,110 | 11,100,110,000 | 11,100,111,101 | 11,111,100,001 | 11,111,101,100 | ||
[1 1 1] | 00000010101 | 00000011000 | 00011000100 | 00011001001 | 00101100111 | 00101101010 | 00110110110 | 00110111011 | |
01000100001 | 01000101100 | 01011110000 | 01011111101 | 01101010011 | 01101011110 | 01110000010 | 01110001111 | ||
10,001,110,000 | 10,001,111,101 | 10,010,100,001 | 10,010,101,100 | 10,100,000,010 | 10,100,001,111 | 10,111,010,011 | 10,111,011,110 | ||
11,001,000,100 | 11,001,001,001 | 11,010,010,101 | 11,010,011,000 | 11,100,110,110 | 11,100,111,011 | 11,111,100,111 | 11,111,101,010 | ||
[1 0 1] | 00000010110 | 00000011011 | 00011000111 | 00011001010 | 00101100100 | 00101101001 | 00110110101 | 00110111000 | |
01000100010 | 01000101111 | 01011110011 | 01011111110 | 01101010000 | 01101011101 | 01110000001 | 01110001100 | ||
10,001,110,011 | 10,001,111,110 | 10,010,100,010 | 10,010,101,111 | 10,100,000,001 | 10,100,001,100 | 10,111,010,000 | 10,111,011,101 | ||
11,001,000,111 | 11,001,001,010 | 11,010,010,110 | 11,010,011,011 | 11,100,110,101 | 11,100,111,000 | 11,111,100,100 | 11,111,101,001 |
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Kang, H., Leng, L. & Chang, CC. Overlapped (7,4) hamming code for large-capacity and low-loss data hiding. Multimed Tools Appl 82, 30345–30374 (2023). https://doi.org/10.1007/s11042-023-14502-1
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DOI: https://doi.org/10.1007/s11042-023-14502-1