On generalized Erd\H{o}s-Ginzburg-Ziv constants for $\mathbb{Z}_2^d$

Let $G$ be a finite abelian group, and $r$ be a multiple of its exponent. The generalized Erd\H{o}s-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 $s_{2 m} (Z_{2}^{d})$ for $d \leq 2m+1$. Connections to linear binary codes of maximal length and codes without a forbidden weight are discussed.

On generalized Erd\H{o}s-Ginzburg-Ziv constants for $Z_{2}^{d}$

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On generalized Erd\H{o}s-Ginzburg-Ziv constants for $Z_{2}^{d}$

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On generalized Erd\H{o}s-Ginzburg-Ziv constants for Z2dZ2d​

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On generalized Erd\H{o}s-Ginzburg-Ziv constants for Z2dZ2d​

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On generalized Erd\H{o}s-Ginzburg-Ziv constants for $Z_{2}^{d}$

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On generalized Erd\H{o}s-Ginzburg-Ziv constants for $Z_{2}^{d}$

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