Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

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

Hrčak ID:

130881

URI

https://hrcak.srce.hr/130881

Datum izdavanja:

18.12.2014.

Posjeta: 561 *