Some designs and codes invariant under the Tits group
Jamshid Moori, Amin Saeidi · Advances in Mathematics of Communications · 2017
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 $^2F_4 \left(2 \right)'$. In particular, we construct a binary code $[1755, 26,1024]_2$ on which $^2F_4 \left(2 \right)'$ acts irreducibly. This is the smallest non-trivial irreducible $GF(2)$-module for our group.