r-fat polynomials are a natural generalization of scattered polynomials. They define linear sets of the projective line PG(1, q(n)) 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 &gt; 0. We completely determine the possible values of r when considering linearized polynomials over F-q4 and we also provide one family of 1-fat polynomials in PG(1, q(5)). Furthermore, we investigate LP polynomials (i.e. polynomials of type f(x) = x + delta x(q2x &amp; nbsp;)is an element of F-qn [x], gcd(n, s) = 1), determining the spectrum of values r for which such polynomials are r-fat. (C)&amp; nbsp;2022 Elsevier Inc. All rights reserved.&amp; nbsp;

### r-fat linearized polynomials over finite fields

#### Abstract

r-fat polynomials are a natural generalization of scattered polynomials. They define linear sets of the projective line PG(1, q(n)) 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 F-q4 and we also provide one family of 1-fat polynomials in PG(1, q(5)). Furthermore, we investigate LP polynomials (i.e. polynomials of type f(x) = x + delta x(q2x & nbsp;)is an element of F-qn [x], gcd(n, s) = 1), determining the spectrum of values r for which such polynomials are r-fat. (C)& nbsp;2022 Elsevier Inc. All rights reserved.& nbsp;
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2022
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11391/1534692`
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