Linear Codes Correcting Repeated Bursts Equipped with Homogeneous Distance

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Theory of Computing Systems Pub Date : 2024-03-06 DOI:10.1007/s00224-024-10166-y

引用次数: 0

Abstract

The homogeneous weight (metric) is useful in the construction of codes over a ring of integers \(\mathbb {Z}_{p^l}\) (p prime and \(l \ge 1\) an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be \(\mathbb {Z}_{4}\) . This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of n-tuples over \(\mathbb {Z}_{p^l}\) . Necessary and sufficient conditions for existence of an (n, k) linear code over \(\mathbb {Z}_{p^l}\) correcting the error patterns with respect to the homogeneous weight are derived.

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利用同质距离校正重复突发的线性编码

Abstract 均质权重（度量）在构建整数环 \(\mathbb {Z}_{p^l}\) 上的编码时非常有用（p 是质数，\(l \ge 1\) 是整数）。当把环看作有限域时，它就变成了哈明权重；当把环看作（（mathbb {Z}_{4}\ ）时，它就变成了李权重。本文提出了在\(\mathbb {Z}_{p^l}\) 上 n 个元组的码空间中突发和重复突发错误的同质权分布和总同质权。推导了在\(\mathbb {Z}_{p^l}\) 上存在一个（n, k）线性码的必要条件和充分条件，该线性码可以纠正与同质权重有关的错误模式。

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

Theory of Computing Systems 工程技术-计算机：理论方法

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： TOCS is devoted to publishing original research from all areas of theoretical computer science, ranging from foundational areas such as computational complexity, to fundamental areas such as algorithms and data structures, to focused areas such as parallel and distributed algorithms and architectures.