Linear complementary dual quasi-cyclic codes of index 2

Kanat Abdukhalikov; Duy Ho; San Ling; Gyanendra K. Verma

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arXiv · 2504.09126

Linear complementary dual quasi-cyclic codes of index 2

Kanat Abdukhalikov·Duy Ho·San Ling·Gyanendra K. Verma

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Abstract

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 of these characterizations, we derive necessary and sufficient conditions for LCD one-generator quasi-cyclic codes. Furthermore, using these characterizations, we construct some new quasi-cyclic LCD codes over small fields.

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Kanat Abdukhalikov, Duy Ho, San Ling, Gyanendra K. Verma. 2025-04-12. Linear complementary dual quasi-cyclic codes of index 2. https://arxiv.org/abs/2504.09126

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