Codes equipped with non-cyclic burst-b distance, bounds and periodical burst errors

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-23 DOI:10.1016/j.cam.2025.117081

Pankaj Kumar Das, Achal Agarwal

引用次数: 0

Abstract

In this paper, we present a study on codes equipped with non-cyclic burst-

b

distance. We mainly study bounds on the maximum number of codewords possible in such a code, as well as the codes’ periodical burst detection- and -correction capability. For such a code, we derive the Litsyn-Laihonen type of bound and its improved version. We also present the asymptotic form of Litsyn-Laihonen type bound and make a comparison with all the previously known asymptotic bounds. We also provide periodical burst detection- and -correction capability for such a code in general and then for a special code. Finally, we give a decoding procedure for the special code along with its computational complexity.

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编码具有非循环突发距离、边界和周期性突发误差

本文研究了具有非循环突发b距离的码。我们主要研究了这种码的最大码字数，以及这种码的周期性突发检测和纠错能力。对于这样的代码，我们导出了界的Litsyn-Laihonen类型及其改进版本。给出了Litsyn-Laihonen型界的渐近形式，并与所有已知的渐近界作了比较。我们还提供定期突发检测和纠正能力，一般这样的代码，然后为特殊代码。最后给出了特殊码的译码过程及其计算复杂度。

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 Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.