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r-fat linearized polynomials over finite fields
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2022-03-01 , DOI: 10.1016/j.jcta.2022.105609
Daniele Bartoli 1 , Giacomo Micheli 2 , Giovanni Zini 3 , Ferdinando Zullo 4
Affiliation  

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 Fq4 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+δxq2sFqn[x], gcd(n,s)=1), determining the spectrum of values r for which such polynomials are r-fat.



中文翻译:

有限域上的 r-fat 线性化多项式

r -fat 多项式是分散多项式的自然推广。他们定义了投影线的线性集PG(1,qn)秩为nr个权重大于 1 的点。使用代数曲线和函数域的技术,我们获得了r的数值界限和不存在异常r -fat 多项式r>0. 当考虑线性化多项式时,我们完全确定了r的可能值Fq4我们还提供了一组 1-fat 多项式PG(1,q5). 此外,我们研究 LP 多项式(即多项式类型F(X)=X+δXq2sFqn[X],gcd(n,s)=1),确定这些多项式为r -fat的值r的频谱。

更新日期:2022-03-01
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