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Coding Matrices for $GL(2,q)$

Year 2018, Volume: 1 Issue: 2, 118 - 130, 25.12.2018
https://doi.org/10.33401/fujma.462055

Abstract

We use the BN-pair structure for the general linear group to write a suitable listing of the elements of the finite group $GL(2,q)$ which is then used to determine its ring of matrices. This approach of identifying finite group ring with ring of matrices has been used effectively to construct linear codes, benefiting from the ring-theoretic structure of both group rings and the ring of matrices.

References

  • [1] F. J. Macwilliams, Codes and ideals in group algebras, Comb. Math. Appl., (1969), 312-328.
  • [2] S. D. Berman, On the theorey of group codes, Kibernetika, 3(1) (1967), 31-39.
  • [3] R. Ferraz, Polcino Milies, Idempotents in group algebras and minimal abelian codes, Finite Fields Appl., 13 (2007), 382-393.
  • [4] T. Hurley, Group rings and ring of matrices, Inter. J. Pure Appl. Math., 31(3) (2006), 319-335.
  • [5] P. Hurley, T. Hurely, Block Codes from Matrix and Group Rings, Chapter 5, (Eds.) I. Woungang, S. Misra, S.C. Misma, Selected Topics in Information and Coding Theory, World Scientific, 2010, 159-194.
  • [6] C. Curtis, I. Reiner, Methods of Representation Theory, Wiley, New York, 1987.
Year 2018, Volume: 1 Issue: 2, 118 - 130, 25.12.2018
https://doi.org/10.33401/fujma.462055

Abstract

References

  • [1] F. J. Macwilliams, Codes and ideals in group algebras, Comb. Math. Appl., (1969), 312-328.
  • [2] S. D. Berman, On the theorey of group codes, Kibernetika, 3(1) (1967), 31-39.
  • [3] R. Ferraz, Polcino Milies, Idempotents in group algebras and minimal abelian codes, Finite Fields Appl., 13 (2007), 382-393.
  • [4] T. Hurley, Group rings and ring of matrices, Inter. J. Pure Appl. Math., 31(3) (2006), 319-335.
  • [5] P. Hurley, T. Hurely, Block Codes from Matrix and Group Rings, Chapter 5, (Eds.) I. Woungang, S. Misra, S.C. Misma, Selected Topics in Information and Coding Theory, World Scientific, 2010, 159-194.
  • [6] C. Curtis, I. Reiner, Methods of Representation Theory, Wiley, New York, 1987.
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ahmed A. Khammash 0000-0001-9404-1732

Marwa M. Hamed This is me 0000-0003-1855-6261

Publication Date December 25, 2018
Submission Date September 21, 2018
Acceptance Date November 15, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Khammash, A. A., & Hamed, M. M. (2018). Coding Matrices for $GL(2,q)$. Fundamental Journal of Mathematics and Applications, 1(2), 118-130. https://doi.org/10.33401/fujma.462055
AMA Khammash AA, Hamed MM. Coding Matrices for $GL(2,q)$. Fundam. J. Math. Appl. December 2018;1(2):118-130. doi:10.33401/fujma.462055
Chicago Khammash, Ahmed A., and Marwa M. Hamed. “Coding Matrices for $GL(2,q)$”. Fundamental Journal of Mathematics and Applications 1, no. 2 (December 2018): 118-30. https://doi.org/10.33401/fujma.462055.
EndNote Khammash AA, Hamed MM (December 1, 2018) Coding Matrices for $GL(2,q)$. Fundamental Journal of Mathematics and Applications 1 2 118–130.
IEEE A. A. Khammash and M. M. Hamed, “Coding Matrices for $GL(2,q)$”, Fundam. J. Math. Appl., vol. 1, no. 2, pp. 118–130, 2018, doi: 10.33401/fujma.462055.
ISNAD Khammash, Ahmed A. - Hamed, Marwa M. “Coding Matrices for $GL(2,q)$”. Fundamental Journal of Mathematics and Applications 1/2 (December 2018), 118-130. https://doi.org/10.33401/fujma.462055.
JAMA Khammash AA, Hamed MM. Coding Matrices for $GL(2,q)$. Fundam. J. Math. Appl. 2018;1:118–130.
MLA Khammash, Ahmed A. and Marwa M. Hamed. “Coding Matrices for $GL(2,q)$”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 118-30, doi:10.33401/fujma.462055.
Vancouver Khammash AA, Hamed MM. Coding Matrices for $GL(2,q)$. Fundam. J. Math. Appl. 2018;1(2):118-30.

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