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- W4381573758 abstract "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 $d_i geq frac{1}{2} sqrt{n_i}$, $n_i$ goes to the infinity for $i=1,2, ldots$, 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 $sqrt{n}-2$. New families of lengths $n=q^m-1$, $m=3, 5, ldots$, self-dual codes over ${bf F}_q$, $q equiv 1$ $mod$ $4$, with their minimum distances larger than or equal to $sqrt{frac{q}{2}}sqrt{n}-q$ are also constructed." @default.
- W4381573758 created "2023-06-22" @default.
- W4381573758 creator A5022499603 @default.
- W4381573758 date "2023-06-20" @default.
- W4381573758 modified "2023-09-24" @default.
- W4381573758 title "New Binary Self-Dual Cyclic Codes with Square-Root-Like Minimum Distances" @default.
- W4381573758 doi "https://doi.org/10.48550/arxiv.2306.11423" @default.
- W4381573758 hasPublicationYear "2023" @default.
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