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<p>We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quasi-cyclic codes of index 2 with respect to the Euclidean, Hermitian, and symplectic inner products. As a consequence, we derive necessary and sufficient conditions for LCD one-generator quasi-cyclic codes. Using these characterizations, we obtain new binary, ternary, and quaternary LCD codes, several of which improve upon the best parameters currently known in the literature.</p>

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Linear complementary dual quasi–cyclic codes of index 2

  • 期刊论文

  • 发表日期：

    2026年5月30日

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  • Kanat Abdukhalikov,
  • Duy Ho,
  • San Ling,
  • Gyanendra K. Verma

摘要

We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quasi-cyclic codes of index 2 with respect to the Euclidean, Hermitian, and symplectic inner products. As a consequence, we derive necessary and sufficient conditions for LCD one-generator quasi-cyclic codes. Using these characterizations, we obtain new binary, ternary, and quaternary LCD codes, several of which improve upon the best parameters currently known in the literature.