Let G be a finite abelian group, and r be a multiple of its exponent. The generalized Erdős–Ginzburg–Ziv constant ${\mathsf{s}}_r(G)$ 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 ${\mathsf{s}}_{2m}({\mathbb{Z}}_2^d)$ for $d\le 2m+1$. Connections to linear binary codes of maximal length and codes without a forbidden weight are discussed.

中文翻译：

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关于广义的Erdős–Ginzburg–Ziv常数 ${\mathbb{ž}}_2^d$

令G为一个有限的阿贝尔群，而r为其指数的倍数。广义Erdős–Ginzburg–Ziv常数${\mathsf{s}}_{\mathrm{[R}}（G）$是最小的整数小号使得长度的每个序列小号超过ģ具有长度的零和子序列- [R 。我们找到的确切值${\mathsf{s}}_{2米}（{\mathbb{ž}}_2^d）$ 对于 $d\le 2米+\mathrm{1个}$。讨论了最大长度的线性二进制代码和没有禁止重量的代码的连接。