Linear complementary dual quasi-cyclic codes of index 2
Information Theory
2026-01-21 v3 math.IT
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.
Keywords
Cite
@article{arxiv.2504.09126,
title = {Linear complementary dual quasi-cyclic codes of index 2},
author = {Kanat Abdukhalikov and Duy Ho and San Ling and Gyanendra K. Verma},
journal= {arXiv preprint arXiv:2504.09126},
year = {2026}
}