Quasi-cyclic codes of index 2
Information Theory
2026-01-21 v1 math.IT
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.
Keywords
Cite
@article{arxiv.2504.00568,
title = {Quasi-cyclic codes of index 2},
author = {Kanat Abdukhalikov and Askar S. Dzhumadil'daev and San Ling},
journal= {arXiv preprint arXiv:2504.00568},
year = {2026}
}