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MacWilliams extension property for arbitrary weights on linear codes over module alphabets
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2021-10-26 , DOI: 10.1007/s10623-021-00945-w
Serhii Dyshko 1 , Jay A. Wood 2
Affiliation  

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.



中文翻译:

用于模块字母表上线性代码的任意权重的 MacWilliams 扩展属性

第一作者最近通过引入与早期方法对偶的行列式标准,证明了配备 Lee 或欧几里德权重的整数残差环上的线性码的扩展定理。在本文中,我们将他的技术推广到字母表上的线性代码的上下文,该字母表是具有循环 socle 并配备任意权重的有限伪注入模块。主要定理是权重具有扩展性的标准。

更新日期:2021-10-26
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