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<p>Cassuto and Blaum introduced symbol-pair codes to address the problem of pair errors in symbol-pair read channels. Maximum distance separable (MDS) symbol-pair codes and almost maximum distance separable (AMDS) symbol-pair codes have good error-correcting capability. In this paper, let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_705_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_q\)</EquationSource> </InlineEquation> be a finite field, where <i>q</i> is a power of a prime <i>p</i> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_705_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="106" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\equiv 1\pmod 6\)</EquationSource> </InlineEquation>, we use repeated-root cyclic codes of length 6<i>p</i> over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_705_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_q\)</EquationSource> </InlineEquation> with Hamming distance <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_705_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(d_H\le 4\)</EquationSource> </InlineEquation> and symbol-pair distance <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_705_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">\(d_p\in \{4,6,7\}\)</EquationSource> </InlineEquation> to construct a new class of MDS symbol-pair codes and four classes of AMDS symbol-pair codes.</p>

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MDS and AMDS symbol-pair cyclic codes of length 6p

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Huan Sun,
  • Fengwei Li,
  • Qin Yue,
  • Binwei Wang

摘要

Cassuto and Blaum introduced symbol-pair codes to address the problem of pair errors in symbol-pair read channels. Maximum distance separable (MDS) symbol-pair codes and almost maximum distance separable (AMDS) symbol-pair codes have good error-correcting capability. In this paper, let \(\mathbb {F}_q\) be a finite field, where q is a power of a prime p and \(p\equiv 1\pmod 6\) , we use repeated-root cyclic codes of length 6p over \(\mathbb {F}_q\) with Hamming distance \(d_H\le 4\) and symbol-pair distance \(d_p\in \{4,6,7\}\) to construct a new class of MDS symbol-pair codes and four classes of AMDS symbol-pair codes.