多倍 1-完美代码

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2024-05-20 DOI:10.1002/jcd.21947

Denis S. Krotov

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引用次数: 0

摘要

任何图中的多倍 1-完美码（用于列表解码的 1-完美码）都是这样一组顶点，即图中的每个顶点与......的元素之间的距离不超过 1。在汉明图（其中为质幂）中，我们描述了多倍 1-完美码的所有参数以及加性多倍 1-完美码的所有参数。特别是，我们证明了加性多重 1-perfect 码与传播的特殊多集广义多线程相关，并且与多重 1-perfect 码相对应的参数多线程总是存在的。

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Multifold 1-perfect codes

A multifold 1-perfect code (1-perfect code for list decoding) in any graph is a set $C$ of vertices such that every vertex of the graph is at distance not more than 1 from exactly $μ$ elements of $C$ . In $q$ -ary Hamming graphs, where $q$ is a prime power, we characterize all parameters of multifold 1-perfect codes and all parameters of additive multifold 1-perfect codes. In particular, we show that additive multifold 1-perfect codes are related to special multiset generalizations of spreads, multispreads, and that multispreads of parameters corresponding to multifold 1-perfect codes always exist.

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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.