This paper presents new upper bounds on the rate of linear $k$-hash codes in $\mathbb{F}_q^n$, $q\geq k$, that is, codes with the property that any $k$ distinct codewords are all simultaneously distinct in at least one coordinate.

翻译：本文给出了 $\mathbb{F}_q^n$ 中线性 $k$ 哈希码（$q\geq k$）的新上界，即具有以下性质的码：任意 $k$ 个不同码字至少在一个坐标上均互不相同。