r-fat polynomials are a natural generalization of scattered polynomials. They define linear sets of the projective line PG(1,qn) of rank n with r points of weight larger than one. Using techniques on algebraic curves and function fields, we obtain numerical bounds for r and the non-existence of exceptional r-fat polynomials with r>0. We completely determine the possible values of r when considering linearized polynomials over Fqjavax.xml.bind.JAXBElement@3a225500 and we also provide one family of 1-fat polynomials in PG(1,q5). Furthermore, we investigate LP-polynomials (i.e. polynomials of type f(x)=x+δxqjavax.xml.bind.JAXBElement@11206662∈Fqjavax.xml.bind.JAXBElement@16c0ec2a[x], gcd(n,s)=1), determining the spectrum of values r for which such polynomials are r-fat.
r-fat linearized polynomials over finite fields / Bartoli, D.; Micheli, G.; Zini, G.; Zullo, F.. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - 189:(2022), pp. 1-30. [10.1016/j.jcta.2022.105609]
r-fat linearized polynomials over finite fields
Zini G.;
2022
Abstract
r-fat polynomials are a natural generalization of scattered polynomials. They define linear sets of the projective line PG(1,qn) of rank n with r points of weight larger than one. Using techniques on algebraic curves and function fields, we obtain numerical bounds for r and the non-existence of exceptional r-fat polynomials with r>0. We completely determine the possible values of r when considering linearized polynomials over Fqjavax.xml.bind.JAXBElement@3a225500 and we also provide one family of 1-fat polynomials in PG(1,q5). Furthermore, we investigate LP-polynomials (i.e. polynomials of type f(x)=x+δxqjavax.xml.bind.JAXBElement@11206662∈Fqjavax.xml.bind.JAXBElement@16c0ec2a[x], gcd(n,s)=1), determining the spectrum of values r for which such polynomials are r-fat.File | Dimensione | Formato | |
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