$GF（3）$、$GF（11）$和$GF（13）上的新线性码$

Q3 Mathematics

Journal of Algebra Combinatorics Discrete Structures and Applications Pub Date : 2019-01-19 DOI:10.13069/JACODESMATH.508968

N. Aydin, Derek Foret

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引用次数: 6

摘要

具有最佳可能参数的线性码的显式构造是编码理论中的一个主要且具有挑战性的问题。循环码及其各种推广，如准扭曲（QT）码，已知包含许多具有最佳参数的码。尽管这些代码类别已经被广泛搜索，但我们已经能够改进现有的搜索算法，以发现字母表$\mathbb上的许多新的线性代码{F}_{3} $，$\mathbb{F}_{11} $和$\mathbb{F}_{13} 具有更好参数的$。给出了三个字母表上总共38个新的线性码。

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

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.

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来源期刊

Journal of Algebra Combinatorics Discrete Structures and Applications Mathematics-Algebra and Number Theory

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

5 weeks