Notes on LCD Codes Over Frobenius Rings

被引：3

作者：

Liu, Zihui ^{[1
]}

Wu, Xin-Wen ^{[2
]}

机构：

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] Indiana Univ Penn, Dept Math & Comp Sci, Indiana, PA 15705 USA

来源：

IEEE COMMUNICATIONS LETTERS | 2021年 / 25卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Liquid crystal displays; Modules (abstract algebra); Linear codes; Generators; Electronic mail; Tools; Finite element analysis; LCD code; Frobenius ring; injective hull; constacyclic code;

D O I：

10.1109/LCOMM.2020.3029073

中图分类号：

TN [电子技术、通信技术];

学科分类号：

0809 ;

摘要：

Let R be a commutative Frobenius local ring. A result that the injective hull of an LCD code C over R is free of dimension l(C), where l(C) is the minimum over the cardinalities of the generating sets of C , is proved in this correspondence. Applying this result, a concise proof for the main result in a recent paper by Sanjit Bhowmick et al. is derived. Furthermore, the LCD lambda-constacyclic codes with lambda being a unit, pi(lambda(2)) = 1 and lambda(2) not equal 1, where pi is the natural projection of R to its residue field, are characterized, as another application of our result.

引用

页码：361 / 364

页数：4

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