Design theory
Designs and their codes
Graph Theory With Applications
Graph Theory With Applications
Some designs and codes invariant under the groups S9 and A8
Designs, Codes and Cryptography
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Let q be a power of 2 greater than 2 and consider the group G = PSL2(q). We choose the maximal subgroups of G isomorphic to the dihedral groups D2(q+1) and D2(q-1) and present the primitive action of G on the right cosets of these two subgroups. We will find the orbits of the point stabilizer in each case and in the case of D2(q-1) we will prove there is an orbit 驴 of the point stabilizer G驴, such that 驴 驴 {驴 } and whose orbiting under G gives a 1-design with the automorphism group isomorphic to the symmetric group $$ \mathbb{S}_{q+1}.$$