Construction of Linear Codes from the Unit Graph G(ℤn)
IF 0.5
Q3 MATHEMATICS
引用次数: 0
Abstract
In this paper, we consider the unit graph [Formula: see text], where [Formula: see text] and [Formula: see text] are distinct primes. For any prime [Formula: see text], we construct [Formula: see text]-ary linear codes from the incidence matrix of the unit graph [Formula: see text] with their parameters. We also prove that the dual of the constructed codes have minimum distance either three or four. Lastly, we stated two conjectures on diameter of unit graph [Formula: see text] and linear codes constructed from the incidence matrix of the unit graph [Formula: see text] for any integer [Formula: see text].用单位图G(n)构造线性码
在本文中，我们考虑单位图[公式:见文]，其中[公式:见文]和[公式:见文]是不同素数。对于任意素数[公式:见文]，我们从单位图[公式:见文]的关联矩阵及其参数构造[公式:见文]-任意线性码。我们还证明了所构造码的对偶最小距离为3或4。最后，我们对任意整数的单位图[公式:见文]的直径和由单位图[公式:见文]的关联矩阵构造的线性码提出了两个猜想[公式:见文]。
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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来源期刊
Asian-European Journal of Mathematics
MATHEMATICS-
CiteScore
1.30
自引率
12.50%
发文量
169
期刊介绍：
Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.
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