New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Nuh Aydin¹  Derek Foret¹ 

[1] Department of Mathematics, Kenyon College

关键词: Best known codes;    Constacyclic codes;    Quasi-cyclic codes;    Quasi-twisted codes;   

DOI  :  10.13069/jacodesmath.508968

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Explicit construction of linear codes with best possible parameters is one of the major and challengingproblems in coding theory. Cyclic codes and their various generalizations, such as quasi-twisted (QT)codes, are known to contain many codes with best known parameters. Despite the fact that theseclasses of codes have been extensively searched, we have been able to refine existing search algorithmsto discover many new linear codes over the alphabets F3, F11, and F13 with better parameters. Atotal of 38 new linear codes over the three alphabets are presented.

【 授权许可】

CC BY