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

Year 2019, Volume: 6 Issue: 1, 13 - 20, 19.01.2019

Nuh Aydin , Derek Foret

https://doi.org/10.13069/jacodesmath.508968

Cited By: 2

Abstract

Explicit construction of linear codes with best possible parameters is one of the major and challenging problems 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 these classes of codes have been extensively searched, we have been able to refine existing search algorithms to discover many new linear codes over the alphabets $\mathbb{F}_{3}$, $\mathbb{F}_{11}$, and $\mathbb{F}_{13}$ with better parameters. A total of 38 new linear codes over the three alphabets are presented.

Keywords

Best known codes, Constacyclic codes, Quasi-cyclic codes, Quasi-twisted codes

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