编码理论在Davenport常数估计中的应用
An application of coding theory to estimating Davenport constants
摘要：
我们研究了达文波特常数的一个公认的推广。对于正整数$j$（情形$j=1$是经典的）和有限阿贝尔群$(G,+,0)$，不变式$\Dav_j(G)$被定义为最小的$\ell$，使得$G$上长度至少为$\ell$的每个序列具有$j$不相交的非空零和序列.我们调查这些数量的基本$2$ -组的大秩（相对于$j$）。使用编码理论的工具，我们对这些数量给出了相当精确的估计。我们使用我们的结果，以改善某些群体的经典达文波特常数的界限。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
