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<p>Symbol-pair codes are proposed to guard against pair-errors in symbol-pair channels, where the outputs are overlapping pairs of symbols. It has been a main problem to find symbol-pair codes with relatively large pair distance. In this paper, we leverage cyclic codes over the finite ring <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{F}_{q}[u]/\langle u^{2}\rangle\)</EquationSource> </InlineEquation> to construct almost MDS symbol-pair codes. A lower bound on the pair distance of the Gray image of a cyclic code over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb{F}_{q}[u]/\langle u^{2}\rangle\)</EquationSource> </InlineEquation> is derived in terms of the Hamming distances of the torsion code and residue code. Almost MDS symbol-pair codes with pair distance <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(8\)</EquationSource> </InlineEquation> are obtained from the Gray images of cyclic codes over <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb{F}_{q}[u]/\langle u^{2}\rangle\)</EquationSource> </InlineEquation>.</p>

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Construction of almost MDS symbol-pair codes via codes over finite rings

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Yiwu Wang,
  • Xiaoshan Kai,
  • Jian Yuan

摘要

Symbol-pair codes are proposed to guard against pair-errors in symbol-pair channels, where the outputs are overlapping pairs of symbols. It has been a main problem to find symbol-pair codes with relatively large pair distance. In this paper, we leverage cyclic codes over the finite ring \(\mathbb{F}_{q}[u]/\langle u^{2}\rangle\) to construct almost MDS symbol-pair codes. A lower bound on the pair distance of the Gray image of a cyclic code over \(\mathbb{F}_{q}[u]/\langle u^{2}\rangle\) is derived in terms of the Hamming distances of the torsion code and residue code. Almost MDS symbol-pair codes with pair distance \(8\) are obtained from the Gray images of cyclic codes over \(\mathbb{F}_{q}[u]/\langle u^{2}\rangle\) .