On equivalence of cyclic codes, generalization of a quasi-twisted search algorithm, and new linear codes

被引：11

作者：

Aydin, Nuh ^{[1
]}

Lambrinos, Jonathan ^{[1
]}

VandenBerg, Oliver ^{[1
]}

机构：

[1] Kenyon Coll, Dept Math & Stat, Gambier, OH 43022 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 10期

关键词：

Best known linear codes; Cyclic codes; Constacyclic codes; Quasi-twisted codes; Equivalence of codes; Search algorithms for linear codes; MINIMUM DISTANCE; OBJECTS;

D O I：

10.1007/s10623-019-00613-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A fundamental problem in coding theory is the explicit construction of linear codes with best possible parameters. A search algorithm (ASR) on certain types of quasi-twisted (QT) codes has been very fruitful to address this challenging problem. In this work, we generalize the ASR algorithm to make it more comprehensive. The generalization is based on code equivalence. As a result of implementing the more general algorithm, we discovered 27 new linear codes over the fields and 7. Further, we prove several useful theoretical results about the equivalence of cyclic codes, constacyclic codes, and QT codes.

引用

页码：2199 / 2212

页数：14

共 33 条

[1] New quinary linear codes from quasi-twisted codes and their duals [J].