Glasnik matematički, Vol. 49 No. 2, 2014.
Original scientific paper
https://doi.org/10.3336/gm.49.2.01
Some irreducible 2-modular codes invariant under the symplectic group S6(2)
Lucy Chikamai
orcid.org/0000-0002-0853-6091
; School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban 4000, South Africa
Jamshid Moori
; School of Mathematical Sciences , North-West University (Mafikeng) , Mmabatho 2735, South Africa
Bernardo G. Rodrigues
orcid.org/0000-0002-1349-0219
; School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban 4000, South Africa
Abstract
We examine all non-trivial binary codes and designs obtained from the 2-modular primitive permutation representations of degrees up to 135 of the simple projective special symplectic group S6(2). The submodule lattice of the permutation modules, together with a comprehensive description of each code including the weight enumerator, the automorphism group, and the action of S6(2) is given. By considering the structures of the stabilizers of several codewords we attempt to gain an insight into the nature of some classes of codewords in particular those of minimum weight.
Keywords
Derived; symmetric and quasi-symmetric designs; self-orthogonal designs; codes; optimal linear code; automorphism group; modular representation; symplectic group
Hrčak ID:
130881
URI
Publication date:
18.12.2014.
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