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<p>In this paper, we establish a new condition for <i>q</i>-ary cyclic codes of length <i>3p</i> to be optimal in the symbol-pair metric. Using this condition, we demonstrate that some AMDS symbol-pair codes of length <i>3p</i> previously obtained are valid not only over the prime field of characteristic <i>p</i> but also over arbitrary finite fields of that characteristic. Furthermore, we construct one new family of AMDS symbol-pair cyclic codes with symbol-pair distance 16. The proposed approach relies on the decomposition of generator polynomials and the analysis of consecutive indices of codewords, leading to sharper lower bounds on symbol-pair distances.</p>

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Optimal symbol-pair constacyclic codes of length \(3p\): new conditions and constructions

  • 期刊论文

  • 发表日期：

    2026年4月24日

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  • Hieu V. Ha

摘要

In this paper, we establish a new condition for q-ary cyclic codes of length 3p to be optimal in the symbol-pair metric. Using this condition, we demonstrate that some AMDS symbol-pair codes of length 3p previously obtained are valid not only over the prime field of characteristic p but also over arbitrary finite fields of that characteristic. Furthermore, we construct one new family of AMDS symbol-pair cyclic codes with symbol-pair distance 16. The proposed approach relies on the decomposition of generator polynomials and the analysis of consecutive indices of codewords, leading to sharper lower bounds on symbol-pair distances.