4 research outputs found
Multi-wise and constrained fully weighted Davenport constants and interactions with coding theory
We consider two families of weighted zero-sum constants for finite abelian groups. For a finite abelian group , a set of weights , and an integral parameter , the -wise Davenport constant with weights is the smallest integer such that each sequence over of length has at least disjoint zero-subsums with weights . And, for an integral parameter , the -constrained Davenport constant with weights is the smallest such that each sequence over of length has a zero-subsum with weights of size at most . First, we establish a link between these two types of constants and several basic and general results on them. Then, for elementary -groups, establishing a link between our constants and the parameters of linear codes as well as the cardinality of cap sets in certain projective spaces, we obtain various explicit results on the values of these constants