Some designs and codes invariant under the tits Group

Abstract

In this paper, we construct some designs and associated binary codes from a primitive permutation representation of degree 1755 of the sporadic simple Tits group 2F4(2)′. In particular, we construct a binary code [1755,26,1024]2 on which 2F4(2)′ acts irreducibly. This is the smallest non-trivial irreducible GF(2)-module for our group.