The parameters of minimal linear codes Let k ≤ n be two positive integers and q a prime power. The basic question in minimal linear codes is to determine if there exists an [ n , k ] q minimal linear code. In this section, we give two theorems and a corollary, which can partially answer this question.
Nov 18, 2019 · The first objective of this paper is to present a new sufficient and necessary condition for linear codes to be minimal. Using this condition, ...
Sep 6, 2024 · The first objective of this paper is to present a new sufficient and necessary condition for linear codes to be minimal. Using this condition, ...
Apr 15, 2024 · In this article, We introduce a condition that is both necessary and sufficient for a linear code to achieve minimality when analyzed over the rings \mathbb{Z} ...
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Abstract— Minimal vectors in linear codes arise in numerous appli- cations, particularly, in constructing decoding algorithms and studying.
Apr 15, 2024 · In this article, We introduce a condition that is both necessary and sufficient for a linear code to achieve minimality when analyzed over ...
The first objective of this paper is to present a new sufficient and necessary condition for linear codes to be minimal. Using this condition, it is easy to ...
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword.
The parameters and weight distribution of Cg(m,k) are given as follows. Theorem 15. The ternary code Cg(m,k) has length 3m −1, dimension m+1, and the weight.
Minimal codes are characterized by the property that none of the codewords is covered by some other linearly independent codeword. We first show that the use ...