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$\mathbb{F}_q^n$（$q\geq k$）上线性$k$-哈希码码率的新上界，即具有如下性质的码：任意$k$个不同码字在至少一个坐标位置上均同时互异。