Maximum flag-rank distance codes

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2024-05-20 DOI:10.1016/j.jcta.2024.105908

Gianira N. Alfarano , Alessandro Neri , Ferdinando Zullo

引用次数: 0

Abstract

In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for network coding. In this setting we provide a Singleton-like bound which relates the parameters of a flag-rank-metric code. This allows us to introduce the family of maximum flag-rank distance codes, that are flag-rank-metric codes meeting the Singleton-like bound with equality. Finally, we provide several constructions of maximum flag-rank distance codes.

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最大旗阶距离编码

在本文中，我们扩展了对赋有旗秩度量的上三角矩阵线性空间的研究。这种度量空间与某些退化旗空间是等距的，并被建议作为网络编码的合适框架。在这种情况下，我们提供了一种类似 Singleton- 的约束，它与旗秩度量编码的参数有关。这样，我们就可以引入最大旗阶距离编码族，即符合辛格列顿类约束的旗阶计量编码。最后，我们提供了几种最大旗阶距离编码的构造。

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

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.