A Carlitz type result for linearized polynomials

Abstract

For an arbitrary $q$-polynomial $f$ over ${\mathbb{F}}_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over ${\mathbb{F}}_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $n\le 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $\mathrm{PG}(1,q^5)$.

References in corpus (1)

• Generalized Twisted Gabidulin Codes

Cited by in corpus (4)

• Vertex properties of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$
• Linear sets and MRD-codes arising from a class of scattered linearized polynomials
• A strengthening of McConnel's theorem on permutations over finite fields
• Generalising the scattered property of subspaces