On the Codes Related to the Higman-Sims Graph

[摘要] All linear codes of length $100$ over a field $F$ which admit the Higman-Sims simple group HS in its rank $3$ representation are determined. By group representation theory it is proved that they can all be understood as submodules of the permutation modul

[学科分类] 离散数学和组合数学

[关键词] Higman-Sims simple group;rank $3$ representation;graph;linear code;Hamming weight;G. Higman's geometry