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<p>Self-orthogonal codes have received much attention in recent years due to their wide-ranging practical applications. The aim of this paper is to construct several infinite families of self-orthogonal codes by using cyclic codes with few nonzeros. We present a sufficient condition for <i>q</i>-ary cyclic codes to&#xa0; be self-orthogonal. Based on this&#xa0; condition, we&#xa0;obtain several families of self-orthogonal cyclic codes over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_q\)</EquationSource> </InlineEquation>. These self-orthogonal codes contain many optimal or best-known codes. The dimensions of these codes are determined and the lower bounds on their minimum distances are given. Numerous examples demonstrate that the lower bounds on the minimum distances of the codes we construct are tight.</p>

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A new construction of self-orthogonal cyclic codes

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Jiayuan Zhang,
  • Xiaoshan Kai,
  • Ting Yao,
  • Ping Li

摘要

Self-orthogonal codes have received much attention in recent years due to their wide-ranging practical applications. The aim of this paper is to construct several infinite families of self-orthogonal codes by using cyclic codes with few nonzeros. We present a sufficient condition for q-ary cyclic codes to  be self-orthogonal. Based on this  condition, we obtain several families of self-orthogonal cyclic codes over \(\mathbb {F}_q\) . These self-orthogonal codes contain many optimal or best-known codes. The dimensions of these codes are determined and the lower bounds on their minimum distances are given. Numerous examples demonstrate that the lower bounds on the minimum distances of the codes we construct are tight.