Codes in Johnson graphs associated with quadratic forms over F2
Mark Ioppolo · UWA Profiles and Research Repository (University of Western Australia) · 2019
This thesis studies strongly incidence-transitive codes in Johnson graphs associated with the 2-transitive actions of Sp(2n,2) of degrees 22n-1±2n-1. We construct two new infinite families of strongly incidence-transitive codes and demonstrate that they are the only examples with codeword stabilisers contained in a geometric Aschbacher class. We construct two additional examples using the fully deleted permutation modules for the symmetric group Sm with m=10 and show no further examples arise for other values of m. If a codeword stabiliser is almost-simple then we show in most cases that the corresponding code cannot be strongly incidence-transitive, though several possibilities remain open.