MacWilliams extension property for arbitrary weights on linear codes over module alphabets

被引：0

作者：

Dyshko, Serhii ^{[1
]}

Wood, Jay A. ^{[1
]}

机构：

[1] Western Michigan Univ, Kalamazoo, MI 49008 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2022年 / 90卷 / 11期

关键词：

Linear code; Extension theorem; Cyclic socle; BI-INVARIANT WEIGHTS; FROBENIUS RINGS; FINITE RINGS; EQUIVALENCE; THEOREM;

D O I：

10.1007/s10623-021-00945-w

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The first author recently proved the extension theorem for linear codes over integer residue rings equipped with the Lee or the Euclidean weight by introducing a determinant criterion that is dual to earlier approaches. In this paper we generalize his techniques to the context of linear codes over an alphabet that is a finite pseudo-injective module with a cyclic socle and is equipped with an arbitrary weight. The main theorem is a criterion for the weight to have the extension property.

引用

页码：2683 / 2701

页数：19

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