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Keywords = one-generator codes

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16 pages, 280 KB  
Article
On Quasi-Cyclic Codes of Index 3
by Kanat Abdukhalikov and Rasha M. Shat
Entropy 2025, 27(11), 1096; https://doi.org/10.3390/e27111096 - 23 Oct 2025
Viewed by 715
Abstract
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated. We give a characterization of self-orthogonal and dual-containing codes. A quasi-cyclic code of [...] Read more.
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated. We give a characterization of self-orthogonal and dual-containing codes. A quasi-cyclic code of index 3 is generated by at most three elements. We describe conditions when such a code (or its dual) is generated by one element. Full article
(This article belongs to the Special Issue Discrete Math in Coding Theory, 2nd Edition)
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