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

Dean Crnković, Vedrana Mikulić Crnković, Andrea Švob

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.

Keywords


Transitive Group, t-Design, Strongly Regular Graph, Distance-Regular Graph, Flag-Transitive Design, Linear Code

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DOI: http://dx.doi.org/10.1478/AAPP.96S2A5

Copyright (c) 2018 Dean Crnković, Vedrana Mikulić Crnković, Andrea Švob

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