纠错和图控制中的线性和非线性环横码

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-03-31 DOI:10.4134/BKMS.B190204

M. Daǧlı, Bokhee Im, Jonathan D. H. Smith

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引用次数: 0

摘要

循环横向码采用纠错码理论的另一种方法，强调要纠正的错误集。到目前为止，循环横向码方法仅限于线性码。本文的目标是扩展环横向码的概念框架，使其能够接受非线性码。我们提出了在循环图中表现出有效支配的完美单错误纠错码中这种非线性的一个自然例子，并将其与类似背景下的线性码进行了对比。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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LINEAR AND NON-LINEAR LOOP-TRANSVERSAL CODES IN ERROR-CORRECTION AND GRAPH DOMINATION

Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).