For an arbitrary $q$-polynomial $f$ over $F_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over $F_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $nleq 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $PG(1,q^5)$. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.
A Carlitz type result for linearized polynomials / Csajbók, Bence; Marino, Giuseppe; Polverino, Olga. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3974. - 16:2(2019), pp. 585-608.
A Carlitz type result for linearized polynomials
Giuseppe Marino;
2019
Abstract
For an arbitrary $q$-polynomial $f$ over $F_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over $F_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $nleq 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $PG(1,q^5)$. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.File in questo prodotto:
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