q-ary (1,k)-overlap-free codes with given restrictions

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-10 DOI:10.1016/j.disc.2024.114236

引用次数: 0

Abstract

Two words u and v have a t-overlap if the length t prefix of u is equal to the length t suffix of v, or vice versa. A code $C$ is t-overlap-free if no two words u and v in $C$ (including $u = v$ ) have a t-overlap. A code of length n is said to be $(t_{1}, t_{2})$ -overlap-free if it is t-overlap-free for all t such that $1 ⩽ t_{1} ⩽ t ⩽ t_{2} ⩽ n - 1$ . A $(1, n - 1)$ -overlap-free code of length n is called non-overlapping, which has applications in DNA-based data storage systems and frame synchronization. In this paper, we initialize the study for codes of length n which are simultaneously $(1, k)$ -overlap-free and $(n - k, n - 1)$ -overlap-free, and establish lower and upper bounds for the size of balanced and error-correcting $(1, k)$ -overlap-free codes.

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具有给定限制条件的 q-ary (1,k) - 无重叠编码

如果 u 的前缀长度 t 等于 v 的后缀长度 t，或反之亦然，则两个词 u 和 v 有 t 重叠。如果 C 中没有两个词 u 和 v（包括 u=v）有 t 重叠，则代码 C 无 t 重叠。如果长度为 n 的代码对所有 t 都是无 t 重叠的，且 1⩽t1⩽t⩽t2⩽n-1。长度为 n 的（1,n-1）无重叠编码称为无重叠编码，它可应用于基于 DNA 的数据存储系统和帧同步。本文初步研究了长度为 n、同时具有 (1,k)-overlap-free 和 (n-k,n-1)-overlap-free 的编码，并建立了平衡编码和纠错 (1,k)-overlap-free 编码大小的下限和上限。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.