Higher Weights of Anticodes and the Generalized Griesmer Bound,

We show that the minimum r-weight dr of an anticode can be expressed in terms of the maximum r-weight of the corresponding code. As examples, we consider anticodes from homogeneous hypersurfaces (quadrics and Hermitian varieties). In a number of cases, all differences (except for one) of the weight hierarchy of such an anticode meet an analog of the generalized Griesmer bound.