Multilayer crisscross error and erasure correction

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-18 DOI:10.1016/j.laa.2025.09.014

Umberto Martínez-Peñas

引用次数: 0

Abstract

In this work, multilayer crisscross errors and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are derived, including a Singleton bound, and maximum multi-cover distance (MMCD) codes are defined as those attaining it. Duality, puncturing and shortening of linear MMCD codes are studied. It is shown that the dual of a linear MMCD code is not necessarily MMCD, and those satisfying this duality condition are defined as dually MMCD codes. Finally, some constructions of codes in the multi-cover metric are given, including dually MMCD codes, together with efficient decoding algorithms for them.

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多层交叉误差和擦除校正

在这项工作中，考虑了多层交叉误差和擦除，它们影响矩阵列表中矩阵的整个行和列。为了测量这种误差和擦除，引入了多覆盖度量。导出了几个边界，包括单例边界，并将最大多覆盖距离（MMCD）代码定义为达到该边界的代码。研究了线性MMCD码的对偶性、穿刺性和缩短性。证明了线性MMCD码的对偶不一定是MMCD，满足对偶条件的定义为对偶MMCD码。最后，给出了多覆盖度量码的一些结构，包括双MMCD码，以及它们的有效解码算法。

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.