Csajbók, Bence and Marino, Giuseppe and Polverino, Olga and Zullo, Ferdinando (2018) A characterization of linearized polynomials with maximum kernel. Finite Fields and their Applications. ISSN 10715797 (In Press)

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Abstract
We provide sufficient and necessary conditions for the coefficients of a qpolynomial f over GF(q^n) which ensure that the number of distinct roots of f in GF(q^n) equals the degree of f. We say that these polynomials have maximum kernel. As an application we study in detail qpolynomials of degree q^(n2) over GF(q^n) which have maximum kernel and for n<7 we list all qpolynomials with maximum kernel. We also obtain information on the splitting field of an arbitrary qpolynomial. Analogous results are proved for q^spolynomials as well, where gcd(s,n) = 1.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria 
Depositing User:  Bence Csajbók 
Date Deposited:  24 Sep 2019 13:53 
Last Modified:  03 Apr 2023 06:33 
URI:  http://real.mtak.hu/id/eprint/100771 
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