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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 S 6 (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 S 6 (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.