An application of coding theory to estimating Davenport constants

Details An application of coding theory to estimating Davenport constants An application of coding theory to estimating Davenport constants

2010-07-01

arxiv.org/abs/1007.0259v1

Mathematics

Number Theory

Scientific paper

We investigate a certain well-established generalization of the Davenport constant. For $j$ a positive integer (the case $j=1$, is the classical one) and a finite Abelian group $(G,+,0)$, the invariant $\Dav_j(G)$ is defined as the smallest $\ell$ such that each sequence over $G$ of length at least $\ell$ has $j$ disjoint non-empty zero-sum subsequences. We investigate these quantities for elementary $2$-groups of large rank (relative to $j$). Using tools from coding theory, we give fairly precise estimates for these quantities. We use our results to give improved bounds for the classical Davenport constant of certain groups.

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