Scholarlink

<p>Symbol-pair codes is a new coding framework that is aimed at preventing pair errors in symbol-pair read channels. A major task of symbol-pair coding theory involves the design of codes, which have a large minimum symbol-pair distance. Particularly, the construction of maximum-distance-separable (MDS) symbol-pair codes, the symbol-pair code with the optimal error-correction capability, has become an open problem. In this paper, four classes of MDS symbol-pair codes of length 4<i>p</i> whose minimum symbol-pair distances are 8, 10, 11 and 12 are obtained by using repeated-root cyclic codes over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_706_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_p\)</EquationSource> </InlineEquation>, where <i>p</i> is an odd prime number. Besides, we derive several classes of almost maximum-distance-separable (AMDS) symbol-pair codes.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

New MDS symbol-pair codes of length 4p from repeated-root cyclic codes

  • 期刊论文

  • 发表日期：

    2025年9月17日

查看全文
  • Xiujing Zheng,
  • Liqi Wang

摘要

Symbol-pair codes is a new coding framework that is aimed at preventing pair errors in symbol-pair read channels. A major task of symbol-pair coding theory involves the design of codes, which have a large minimum symbol-pair distance. Particularly, the construction of maximum-distance-separable (MDS) symbol-pair codes, the symbol-pair code with the optimal error-correction capability, has become an open problem. In this paper, four classes of MDS symbol-pair codes of length 4p whose minimum symbol-pair distances are 8, 10, 11 and 12 are obtained by using repeated-root cyclic codes over \(\mathbb {F}_p\) , where p is an odd prime number. Besides, we derive several classes of almost maximum-distance-separable (AMDS) symbol-pair codes.