An application of coding theory to estimating Davenport constants

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 D j ( G ) is defined as the smallest ℓ such that each sequence over G of length at least ℓ has j...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2011, Vol.61 (1), p.105-118
Main Authors: Plagne, Alain, Schmid, Wolfgang A.
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Mathematics
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Summary: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 D j ( G ) is defined as the smallest ℓ such that each sequence over G of length at least ℓ 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.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-010-9441-5