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.
[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
[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.
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.