r-fat linearized polynomials over finite fields

r -fat polynomials are a natural generalization of scattered polynomials. They define linear sets the projective line PG ( 1 , q n ) rank with points weight larger than one. Using techniques on algebraic curves and function fields, we obtain numerical bounds for non-existence exceptional > 0 . We completely determine possible values when considering linearized over F 4 also provide one family 1-fat in 5 Furthermore, investigate LP-polynomials (i.e. type f x = + δ 2 s ∈ [ ] gcd ⁡ ), determining spectrum which such -fat.