Glasnik Matematicki, Vol. 49, No. 2 (2014), 235-262.

SOME IRREDUCIBLE 2-MODULAR CODES INVARIANT UNDER THE SYMPLECTIC GROUP S₆(2)

Lucy Chikamai, Jamshid Moori and Bernardo G. Rodrigues

School of Mathematical Sciences , North-West University (Mafikeng) , Mmabatho 2735, South Africa
e-mail: Jamshid.Moori@nwu.ac.za

School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban 4000, South Africa
e-mail: rodrigues@ukzn.ac.za

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.

2010 Mathematics Subject Classification.   05B05, 20D45, 94B05.

Key words and phrases.   Derived, symmetric and quasi-symmetric designs, self-orthogonal designs, codes, optimal linear code, automorphism group, modular representation, symplectic group.

DOI: 10.3336/gm.49.2.01

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