Optimal binary and ternary linear codes with hull dimension one

被引：7

作者：

Mankean, Todsapol ^{[1
]}

Jitman, Somphong ^{[1
]}

机构：

[1] Silpakorn Univ, Fac Sci, Dept Math, Amphoe Muang 73000, Nakhon Pathom, Thailand

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2020年 / 64卷 / 1-2期

关键词：

Linear codes; Optimal linear codes; Griesmer bound; Euclidean inner product; Hermitian inner product; Hulls; Hull dimensions; LCD CODES; PERMUTATION; EQUIVALENT;

D O I：

10.1007/s12190-020-01348-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Hulls of linear codes have been of interest and extensively studied due to their wide applications. In this paper, we focus on constructions and optimality of linear codes with hull dimension one over small finite fields. General constructions for such codes are given together with the analysis on their parameters. Optimal linear [n, 2, d](q) codes with hull dimension one are presented for all positive integers n >= 3 and q is an element of {2, 3}. Moreover, for q = 2, the enumeration of such optimal codes is given up to equivalence.

引用

页码：137 / 155

页数：19

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