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Open AccessArticle
Matrix Factorization and Some Fast Discrete Transforms
by
Iliya Bouyukliev
Iliya Bouyukliev 1,*
,
Mariya Dzhumalieva-Stoeva
Mariya Dzhumalieva-Stoeva 2
and
Paskal Piperkov
Paskal Piperkov 2
1
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
2
Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5003 Veliko Tarnovo, Bulgaria
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(8), 495; https://doi.org/10.3390/axioms13080495 (registering DOI)
Submission received: 4 July 2024
/
Revised: 18 July 2024
/
Accepted: 21 July 2024
/
Published: 23 July 2024
Abstract
In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered transforms in coding theory for calculating the weight distribution of a linear code.
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MDPI and ACS Style
Bouyukliev, I.; Dzhumalieva-Stoeva, M.; Piperkov, P.
Matrix Factorization and Some Fast Discrete Transforms. Axioms 2024, 13, 495.
https://doi.org/10.3390/axioms13080495
AMA Style
Bouyukliev I, Dzhumalieva-Stoeva M, Piperkov P.
Matrix Factorization and Some Fast Discrete Transforms. Axioms. 2024; 13(8):495.
https://doi.org/10.3390/axioms13080495
Chicago/Turabian Style
Bouyukliev, Iliya, Mariya Dzhumalieva-Stoeva, and Paskal Piperkov.
2024. "Matrix Factorization and Some Fast Discrete Transforms" Axioms 13, no. 8: 495.
https://doi.org/10.3390/axioms13080495
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