A Carlitz type result for linearized polynomials - Csajbók, Bence (Ars mathematica contemporanea, 2019)
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 ?$n ≤ 5$? we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of ?$PG(1, q^5)$?.
Keywords: direction; linear set; linearized polynomial; linearizirani polinom; linearna množica; smer