MDS代码和拉丁立方体中的嵌入

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-06-20 DOI:10.1002/jcd.21849

Vladimir N. Potapov

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引用次数: 2

摘要

代码的嵌入是一种保持码字之间距离的映射。我们证明了任何具有码距d$d$和长度n$n$的码都可以嵌入到具有相同码距和长度但在较大字母表下的最大距离可分离（MDS）码中。作为一个推论，我们得到了部分相互正交拉丁立方体和n$n$-元拟群的系统的嵌入。

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Embedding in MDS codes and Latin cubes

An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $d$ and length $n$ can be embedded into an maximum distance separable (MDS) code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and $n$ -ary quasigroups.

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.