Some designs and codes invariant under the Tits group. (English) Zbl 1357.05019
Summary: 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 \({}^2F_4(2)'\). In particular, we construct a binary code \([1755, 26,1024]_2\) on which \({}^2F_4(2)'\) acts irreducibly. This is the smallest non-trivial irreducible \(\mathrm{GF}(2)\)-module for our group.
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 20D05 | Finite simple groups and their classification |
Keywords:
Tits group; symmetric designs; primitive permutation representations; linear codes; irreducible \(G\)-modulesReferences:
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