Research Article
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Year 2024, Early Access, 1 - 14
https://doi.org/10.24330/ieja.1596075

Abstract

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.

Group structures of twistulant matrices over rings

Year 2024, Early Access, 1 - 14
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.

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.
There are 11 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

H.tapia Recillas

J. Armando Velazco - Velazco This is me

Early Pub Date December 4, 2024
Publication Date
Submission Date April 20, 2024
Acceptance Date September 15, 2024
Published in Issue Year 2024 Early Access

Cite

APA Recillas, H., & Velazco - Velazco, J. A. (2024). Group structures of twistulant matrices over rings. International Electronic Journal of Algebra1-14. https://doi.org/10.24330/ieja.1596075
AMA Recillas H, Velazco - Velazco JA. Group structures of twistulant matrices over rings. IEJA. Published online December 1, 2024:1-14. doi:10.24330/ieja.1596075
Chicago Recillas, H.tapia, and J. Armando Velazco - Velazco. “Group Structures of Twistulant Matrices over Rings”. International Electronic Journal of Algebra, December (December 2024), 1-14. https://doi.org/10.24330/ieja.1596075.
EndNote Recillas H, Velazco - Velazco JA (December 1, 2024) Group structures of twistulant matrices over rings. International Electronic Journal of Algebra 1–14.
IEEE H. Recillas and J. A. Velazco - Velazco, “Group structures of twistulant matrices over rings”, IEJA, pp. 1–14, December 2024, doi: 10.24330/ieja.1596075.
ISNAD Recillas, H.tapia - Velazco - Velazco, J. Armando. “Group Structures of Twistulant Matrices over Rings”. International Electronic Journal of Algebra. December 2024. 1-14. https://doi.org/10.24330/ieja.1596075.
JAMA Recillas H, Velazco - Velazco JA. Group structures of twistulant matrices over rings. IEJA. 2024;:1–14.
MLA Recillas, H.tapia and J. Armando Velazco - Velazco. “Group Structures of Twistulant Matrices over Rings”. International Electronic Journal of Algebra, 2024, pp. 1-14, doi:10.24330/ieja.1596075.
Vancouver Recillas H, Velazco - Velazco JA. Group structures of twistulant matrices over rings. IEJA. 2024:1-14.