Generator matrices of quasi-cyclic codes

Date

2026-11-01

Author

Bayraktar, Gözde Cennet
Özbudak, Ferruh
Özkaya, Buket

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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In this paper, we provide a complete solution to an open problem by applying the spectral method to the polynomial generator matrices of quasi-cyclic codes of arbitrary index, using the corresponding reduced Gröbner basis of the given quasi-cyclic code. More precisely, with this method, we construct a full generator matrix over the suitable extension field. We provide two explicit examples to illustrate the construction of a full generator matrix from the given polynomial generator matrix of the code in the cases of index 2 and index 3, respectively. Furthermore, we investigate the reduced Gröbner basis of the subclass of 2D-cyclic codes of index 2 and index 3, proving that they have polynomial generator matrices in diagonal form.

Subject Keywords

Generator matrix, Quasi-cyclic codes, Spectral analysis

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105040098169&origin=inward
https://hdl.handle.net/11511/119559

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Graduate School of Applied Mathematics, Article