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https://doi.org/10.3336/gm.47.2.01

2-modular representations of the alternating group A_8 as binary codes

L. Chikamai ; School of Mathematical Sciences , University of KwaZulu-Natal , Durban 4041, South Africa
Jamshid Moori ; School of Mathematical Sciences , North-West University (Mafikeng) , Mmabatho 2735, South Africa
B. G. Rodrigues   ORCID icon orcid.org/0000-0002-1349-0219 ; School of Mathematical Sciences , University of KwaZulu-Natal , Durban 4041, South Africa

Puni tekst: engleski, pdf (295 KB) str. 225-252 preuzimanja: 388* citiraj
APA 6th Edition
Chikamai, L., Moori, J. i Rodrigues, B.G. (2012). 2-modular representations of the alternating group A_8 as binary codes. Glasnik matematički, 47 (2), 225-252. https://doi.org/10.3336/gm.47.2.01
MLA 8th Edition
Chikamai, L., et al. "2-modular representations of the alternating group A_8 as binary codes." Glasnik matematički, vol. 47, br. 2, 2012, str. 225-252. https://doi.org/10.3336/gm.47.2.01. Citirano 27.10.2021.
Chicago 17th Edition
Chikamai, L., Jamshid Moori i B. G. Rodrigues. "2-modular representations of the alternating group A_8 as binary codes." Glasnik matematički 47, br. 2 (2012): 225-252. https://doi.org/10.3336/gm.47.2.01
Harvard
Chikamai, L., Moori, J., i Rodrigues, B.G. (2012). '2-modular representations of the alternating group A_8 as binary codes', Glasnik matematički, 47(2), str. 225-252. https://doi.org/10.3336/gm.47.2.01
Vancouver
Chikamai L, Moori J, Rodrigues BG. 2-modular representations of the alternating group A_8 as binary codes. Glasnik matematički [Internet]. 2012 [pristupljeno 27.10.2021.];47(2):225-252. https://doi.org/10.3336/gm.47.2.01
IEEE
L. Chikamai, J. Moori i B.G. Rodrigues, "2-modular representations of the alternating group A_8 as binary codes", Glasnik matematički, vol.47, br. 2, str. 225-252, 2012. [Online]. https://doi.org/10.3336/gm.47.2.01

Sažetak
Through a modular representation theoretical approach we enumerate all non-trivial codes from the 2-modular representations of A8, using a chain of maximal submodules of a permutation module induced by the action of A8 on objects such as points, Steiner S(3,4,8) systems, duads, bisections and triads. Using the geometry of these objects we attempt to gain some insight into the nature of possible codewords, particularly those of minimum weight. Several sets of non-trivial codewords in the codes examined constitute single orbits of the automorphism groups that are stabilized by maximal subgroups. Many self-orthogonal codes invariant under A8 are obtained, and moreover, 22 optimal codes all invariant under A8 are constructed. Finally, we establish that there are no self-dual codes of lengths 28 and 56 invariant under A8 and S8 respectively, and in particular no self-dual doubly-even code of length 56.

Ključne riječi
Derived; symmetric and quasi-symmetric designs; self-orthogonal designs; codes; optimal linear code; automorphism group; modular representation; alternating group

Hrčak ID: 93938

URI
https://hrcak.srce.hr/93938

Posjeta: 627 *