New Binary Self-Dual Cyclic Codes with Square-Root-Like Minimum Distances

06/20/2023

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by   Hao Chen, et al.

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The construction of self-dual codes over small fields such that their minimum distances are as large as possible is a long-standing challenging problem in the coding theory. In 2009, a family of binary self-dual cyclic codes with lengths n_i and minimum distances d_i ≥1/2√(n_i), n_i goes to the infinity for i=1,2, …, was constructed. In this paper, we construct a family of (repeated-root) binary self-dual cyclic codes with lengths n and minimum distances at least √(n)-2. New families of lengths n=q^m-1, m=3, 5, …, self-dual codes over F_q, q ≡ 1 mod 4, with their minimum distances larger than or equal to √(q/2)√(n)-q are also constructed.