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.
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页码：2683 / 2701
页数：19
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