Abstract
In this paper, we propose a class of binary sequences induced by monomial permutation polynomials over \(\mathrm {GF}(2^{p})\) and study the period property and the shift-equivalence of these binary sequences. In particularly, we give a necessary and sufficient condition for such a sequence to have maximal period. Moreover, we also give a necessary and sufficient condition for two such sequences to be shift equivalent.
This work was supported by NSF of China (Nos. 61872383). The work of Qun-Xiong Zheng was also supported by Young Elite Scientists Sponsorship Program by CAST (2016QNRC001) and by National Postdoctoral Program for Innovative Talents (BX201600188) and by China Postdoctoral Science Foundation funded project (2017M611035).
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The authors would like to thank the anonymous referees for their helpful comments and suggestions.
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Zheng, QX., Jiang, Y., Lin, D., Qi, WF. (2021). Binary Sequences Derived from Monomial Permutation Polynomials over GF(2\(^{p}\)). In: Yu, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2021. Lecture Notes in Computer Science(), vol 13007. Springer, Cham. https://doi.org/10.1007/978-3-030-88323-2_20
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DOI: https://doi.org/10.1007/978-3-030-88323-2_20
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