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Coding Matrices for $GL(2,q)$

Yıl 2018, Cilt: 1 Sayı: 2, 118 - 130, 25.12.2018
https://doi.org/10.33401/fujma.462055

Öz

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.

Kaynakça

  • [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.
Yıl 2018, Cilt: 1 Sayı: 2, 118 - 130, 25.12.2018
https://doi.org/10.33401/fujma.462055

Öz

Kaynakça

  • [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.
Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ahmed A. Khammash 0000-0001-9404-1732

Marwa M. Hamed Bu kişi benim 0000-0003-1855-6261

Yayımlanma Tarihi 25 Aralık 2018
Gönderilme Tarihi 21 Eylül 2018
Kabul Tarihi 15 Kasım 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

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. Aralık 2018;1(2):118-130. doi:10.33401/fujma.462055
Chicago Khammash, Ahmed A., ve Marwa M. Hamed. “Coding Matrices for $GL(2,q)$”. Fundamental Journal of Mathematics and Applications 1, sy. 2 (Aralık 2018): 118-30. https://doi.org/10.33401/fujma.462055.
EndNote Khammash AA, Hamed MM (01 Aralık 2018) Coding Matrices for $GL(2,q)$. Fundamental Journal of Mathematics and Applications 1 2 118–130.
IEEE A. A. Khammash ve M. M. Hamed, “Coding Matrices for $GL(2,q)$”, Fundam. J. Math. Appl., c. 1, sy. 2, ss. 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 (Aralık 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. ve Marwa M. Hamed. “Coding Matrices for $GL(2,q)$”. Fundamental Journal of Mathematics and Applications, c. 1, sy. 2, 2018, ss. 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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