Generator Matrices of Quasi-Cyclic Codes

Date

2025-8-27

Author

Bayraktar, Gözde Cennet

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We give a complete solution to an open problem by using the spectral method on the polynomial generator matrices of quasi-cyclic codes of an arbitrary index, with the corresponding reduced Gröbner basis of the given quasi-cyclic code. To be more specific, we construct a full generator matrix over a suitable extension field of the given base field using this method. For indices 2 and 3, we demonstrate two respective examples to show how we construct the full generator matrix from the given polynomial generator matrix. Moreover, we show that the reduced Gröbner basis of the subclass of 2D-cyclic codes should provide a polynomial generator matrix in diagonal form in the cases of index 2 and index 3.

Subject Keywords

Quasi-cyclic codes, spectral analysis, generator matrix

URI

https://hdl.handle.net/11511/115695

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Graduate School of Applied Mathematics, Thesis