A class of scattered linearized polynomials covering infinitely many field extensions is exhibited. More precisely, the q-polynomial over \({{\mathbb {F}}}_{q^6}\), \(q \equiv 1\pmod 4\) described in Bartoli et al. (ARS Math Contemp 19:125–145, 2020) and Zanella and Zullo (Discrete Math 343:111800, 2020) is generalized for any even \(n\ge 6\) to an \({{{\mathbb {F}}}_q}\)-linear automorphism \(\psi (x)\) of \({{\mathbb {F}}}_{q^n}\) of order n. Such \(\psi (x)\) and some functional powers of it are proved to be scattered. In particular, this provides new maximum scattered linear sets of the projective line \({{\,\mathrm{{PG}}\,}}(1,q^n)\) for \(n=8,10\). The polynomials described in this paper lead to a new infinite family of MRD-codes in \({{\mathbb {F}}}_q^{n\times n}\) with minimum distance \(n-1\) for any odd q if \(n\equiv 0\pmod 4\) and any \(q\equiv 1\pmod 4\) if \(n\equiv 2\pmod 4\).

一类分散的线性化多项式，涵盖了无限多个场扩展。更准确地说，在Bartoli等人中描述的\（{{\ mathbb {F}}} _ {q ^ 6} \），\（q \ equiv 1 \ pmod 4 \）上的q多项式。（ARS Math Contemp 19：125–145，2020）和Zanella和Zullo（Discrete Math 343：111800，2020）对于任何偶数\（n \ ge 6 \）都可以推广为\（{{{\ mathbb {F} }} _ q} \） -阶n的\（{{\ mathbb {F}}} __ {q ^ n} \）的线性自同构\（\ psi（x）\）。这样的\（\ psi（x）\）并且它的某些功能被证明是分散的。特别是，这为\（n = 8,10 \）提供了投影线\（{{\，\ mathrm {{PG}} \，}}（1，q ^ n）\）的新的最大分散线性集。本文描述的多项式在\（{{\ mathbb {F}}} _ q ^ {n \ times n} \）中导致了一个新的无穷大MRD码族，对于任何对象，最小距离为\（n-1 \）奇q如果\（N \当量0 \ PMOD 4 \）和任何\（q \当量1 \ PMOD 4 \）如果\（N \当量2 \ PMOD 4 \） 。