MODULAR ELEMENTS OF HIGHER-WEIGHT DOWLING LATTICES

The higher-weight Dowling lattice L(k) is the geometric lattice consis ting of those subspaces of the vector space V(n)(q) which have bases o f weight k or less, with these subspaces ordered by inclusion. These l attices arise when Crapo and Rota's results on the critical problem ar e applied to the fundamental problem of linear coding theory. This pap er identifies the modular elements of higher-weight Dowling lattices a nd applies that analysis to modular complements in L(k) and to the cha racteristic polynomial of L(k).