On Quasi-Cyclic Codes of Index 3

Kanat Abdukhalikov; Rasha M. Shat

doi:10.3390/e27111096

On Quasi-Cyclic Codes of Index 3

Kanat Abdukhalikov
, Rasha M. Shat

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 index 3 is generated by at most three elements. We describe conditions when such a code (or its dual) is generated by one element.

Original language	English
Article number	1096
Journal	Entropy
Volume	27
Issue number	11
DOIs	https://doi.org/10.3390/e27111096
Publication status	Published - Nov 2025

Keywords

dual codes
one-generator codes
quasi-cyclic codes

ASJC Scopus subject areas

Information Systems
Mathematical Physics
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Electrical and Electronic Engineering

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10.3390/e27111096

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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 index 3 is generated by at most three elements. We describe conditions when such a code (or its dual) is generated by one element.",

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AB - 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.

KW - dual codes

KW - one-generator codes

KW - quasi-cyclic codes

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U2 - 10.3390/e27111096

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VL - 27

JO - Entropy

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On Quasi-Cyclic Codes of Index 3

Abstract

Keywords

ASJC Scopus subject areas

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