Transitive combinatorial structures invariant under some subgroups of S(6,2) and related codes

Abstract

In this paper we define combinatorial structures on the conjugacy classes of the maximal subgroups of the symplectic group S(6,2) under the action of two subgroups of S(6,2) isomorphic to U(3,3) or U(4,2). Further, we examine binary and ternary linear codes obtained from the row span of the incidence matrices of the block designs (respectively adjacency matrices of the strongly regular graphs) obtained in the paper. Moreover, from the codes examined we construct the designs supported by the codewords as well as SRG and DRG, respectively.