paper

Quasi-cyclic codes of index 2

arXiv:2504.00568 · doi:10.1016/j.disc.2026.115004

Abstract

We study quasi-cyclic codes of index 2 over finite fields. We give a classification of such codes. Their duals with respect to the Euclidean, symplectic and Hermitian inner products are investigated. We describe self-orthogonal and dual-containing codes. Lower bounds for minimum distances of quasi-cyclic codes are given. A quasi-cyclic code of index 2 is generated by at most two elements. We describe conditions when such a code (or its dual) is generated by one element.

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