ON THE GENERALISED RANK WEIGHTS OF QUASI-CYCLIC CODES

被引：0

作者：

Lim, Enhui ^{[1
]}

Oggier, Frederique ^{[1
]}

机构：

[1] Nanyang Technol Univ, Div Math Sci, Singapore, Singapore

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2024年 / 18卷 / 01期

关键词：

Bounds; Generalized rank weights; Rank distance; Quasi-cyclic codes; ALGEBRAIC STRUCTURE;

D O I：

10.3934/amc.2022010

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Generalised rank weights were formulated in analogy to Wei's generalised Hamming weights, but for the rank metric. In this paper we study the generalised rank weights of quasi-cyclic codes, a special class of linear codes usually studied for their properties in error correction over the Hamming metric. By using the algebraic structure of quasi-cyclic codes, a new upper bound on the generalised rank weights of quasi-cyclic codes is formulated, which is tighter than the known Singleton bound. Additionally, it is shown that the first generalised rank weight of self-dual 1-generator quasi-cyclic codes is almost completely determined by the choice of F-qm.

引用

页码：192 / 205

页数：14

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