On generalized Erdős-Ginzburg-Ziv constants for ${\mathbb{Z}}_2^d$

Abstract

Let $G$ be a finite abelian group, and $r$ be a multiple of its exponent. The generalized Erdős-Ginzburg-Ziv constant $s_r(G)$ is the smallest integer $s$ such that every sequence of length $s$ over $G$ has a zero-sum subsequence of length $r$. We find exact values of $s_{2m}({\mathbb{Z}}_2^d)$ for $d\le 2m+1$. Connections to linear binary codes of maximal length and codes without a forbidden weight are discussed.

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