We provide sufficient and necessary conditions for the coefficients of a q-polynomial f over Fqjavax.xml.bind.JAXBElement@3cfd4151 which ensure that the number of distinct roots of f in Fq^n equals the degree of f. We say that these polynomials have maximum kernel. As an application we study in detail q-polynomials of degree q^(n−2) over Fq^n which have maximum kernel and for n≤6 we list all q-polynomials with maximum kernel. We also obtain information on the splitting field of an arbitrary q-polynomial. Analogous results are proved for q^s-polynomials as well, where gcd(s,n)=1.
A characterization of linearized polynomials with maximum kernel
Csajbok, Bence;
2019-01-01
Abstract
We provide sufficient and necessary conditions for the coefficients of a q-polynomial f over Fqjavax.xml.bind.JAXBElement@3cfd4151 which ensure that the number of distinct roots of f in Fq^n equals the degree of f. We say that these polynomials have maximum kernel. As an application we study in detail q-polynomials of degree q^(n−2) over Fq^n which have maximum kernel and for n≤6 we list all q-polynomials with maximum kernel. We also obtain information on the splitting field of an arbitrary q-polynomial. Analogous results are proved for q^s-polynomials as well, where gcd(s,n)=1.File in questo prodotto:
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