A linearized polynomial $f(x)\in {\mathbb{F}}_{q^n}[x]$ is called scattered if for any $y,z\in {\mathbb{F}}_{q^n}$, the condition $zf(y)-yf(z)=0$ implies that y and z are ${\mathbb{F}}_q$-linearly dependent. In this paper two generalizations of the notion of a scattered linearized polynomial are provided and investigated. Let t be a nontrivial positive divisor of n. By weakening the property defining a scattered linearized polynomial, $\mathrm{L-}{q}^t$-partially scattered and $\mathrm{R-}{q}^t$-partially scattered linearized polynomials are introduced in such a way that the scattered linearized polynomials are precisely those which are both $\mathrm{L-}{q}^t$- and $\mathrm{R-}{q}^t$-partially scattered. Also, connections between partially scattered polynomials, linear sets and rank metric codes are exhibited.

线性化多项式 $F(X)\in {\mathbb{F}}_{q^n}[X]$ 如果有任何，则称为分散 $是,z\in {\mathbb{F}}_{q^n}$， 条件 $zF(是)-是F(z)=0$意味着y和z是${\mathbb{F}}_q$- 线性相关。在本文中，提供并研究了散射线性化多项式概念的两种推广。令t是n的非平凡正除数。通过弱化定义分散线性化多项式的属性，$\mathrm{L-}{q}^{吨}$- 部分分散和 $\mathrm{R-}{q}^{吨}$- 部分分散的线性化多项式的引入方式是，分散的线性化多项式恰好是那些既是 $\mathrm{L-}{q}^{吨}$- 和 $\mathrm{R-}{q}^{吨}$- 部分分散。此外，还展示了部分分散多项式、线性集和秩度量代码之间的联系。