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Article Dans Une Revue Journal of Combinatorial Theory, Series A Année : 2015

Multi-wise and constrained fully weighted Davenport constants and interactions with coding theory

Résumé

We consider two families of weighted zero-sum constants for finite abelian groups. For a finite abelian group $( G , + )$, a set of weights $W \subset \mathbb{Z}$, and an integral parameter $m$, the $m$-wise Davenport constant with weights $W$ is the smallest integer $n$ such that each sequence over $G$ of length $n$ has at least $m$ disjoint zero-subsums with weights $W$. And, for an integral parameter $d$, the $d$-constrained Davenport constant with weights $W$ is the smallest $n$ such that each sequence over $G$ of length $n$ has a zero-subsum with weights $W$ of size at most $d$. First, we establish a link between these two types of constants and several basic and general results on them. Then, for elementary $p$-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.
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Dates et versions

hal-01020156 , version 1 (07-07-2014)
hal-01020156 , version 2 (19-05-2015)

Identifiants

Citer

Luz Elimar Marchan, Oscar Ordaz, Irene Santos, Wolfgang Schmid. Multi-wise and constrained fully weighted Davenport constants and interactions with coding theory. Journal of Combinatorial Theory, Series A, 2015, 135, pp.237-267. ⟨10.1016/j.jcta.2015.05.004⟩. ⟨hal-01020156v2⟩
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