Group structures of twistulant matrices over rings

Year 2025, Volume: 38 Issue: 38, 90 - 103, 14.07.2025

H.tapia Recillas , J. Armando Velazco - Velazco

https://doi.org/10.24330/ieja.1596075

Abstract

In this work the algebraic structures of twistulant matrices defined over a ring are studied, with particular attention on their multiplicative structure. It is determined these matrices over a ring are an abelian group and when they are defined over a field the diagonalization of such matrices is considered.

Keywords

Twistulant matrix, discrete Fourier transform, finite field

References

• N. Aydin, N. Connolly and M. Grassl, Some results on the structure of constacyclic codes and new linear codes over $GF(7)$ from quasi-twisted codes, Adv. Math. Commun., 11(1) (2017), 245-258.
• R. E. Blahut, Algebraic Codes on Lines, Planes and Curves: An Engineering Approach, Cambridge University Press, Cambridge, 2008.
• B. Chen, Y. Fan, L. Lin and H. Liu, Constacyclic codes over finite fields, Finite Fields Appl., 18(6) (2012), 1217-1231.
• P. J. Davis, Circulant Matrices, A Wiley-Interscience Publication, Pure and Applied Mathematics, John Wiley \& Sons, New York-Chichester-Brisbane, 1979.
• Discrete Fourier Transform, (2024, February 15) in Wikipedia, https://en.wikipedia.org/wiki/DFT\_matrix.
• S. Jitman, S. Ruangpum and T. Ruangtrakul, Group structures of complex twistulant matrices, AIP Conf. Proc., 1775 (2016), 030016 (8 pp).
• S. Jitman, Vector-circulant matrices and vector-circulant based additive codes over finite fields, Information, 8(3) (2017), 82 (7 pp).
• I. Kra and S. R. Simanca, On circulant matrices, Notices Amer. Math. Soc., 59(3) (2012), 368-377.
• F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, New York: Elsevier/North Holland, 1977.
• H. Tapia-Recillas and J. A. Velazco-Velazco, Diagonalizacion de matrices circulantes por medio de la Transformada Discreta de Fourier sobre campos finitos, Rev. Met. de Mat., 13(1) (2022), 95-98.
• The Sage Developers, SageMath, the Sage Mathematics Software System (Version 10.0) (2023), https://www.sagemath.org.