For an arbitrary q-polynomial f over GF(q^n) we study the problem of finding those q-polynomials g over GF(q^n) for which the image sets of f(x)/x and g(x)/x coincide. For n < 6 we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of PG(1,q^5).
Csajbók, Bence and Marino, Giuseppe and Polverino, Olga (2019) A Carlitz type result for linearized polynomials. Ars Mathematica Contemporanea. ISSN 1855-3966
