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On the classification of exceptional scattered polynomials
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2020-12-15 , DOI: 10.1016/j.jcta.2020.105386
Daniele Bartoli , Maria Montanucci

Let f(X)Fqr[X] be a q-polynomial. If the Fq-subspace U={(xqt,f(x))|xFqn} defines a maximum scattered linear set, then we call f(X) a scattered polynomial of index t. The asymptotic behavior of scattered polynomials of index t is an interesting open problem. In this sense, exceptional scattered polynomials of index t are those for which U is a maximum scattered linear set in PG(1,qmr) for infinitely many m. The classifications of exceptional scattered monic polynomials of index 0 (for q>5) and of index 1 were obtained in [1]. In this paper we complete the classifications of exceptional scattered monic polynomials of index 0 for q4. Also, some partial classifications are obtained for arbitrary t. As a consequence, the classification of exceptional scattered monic polynomials of index 2 is given.



中文翻译:

关于特殊分散多项式的分类

FXFq[R[X]q多项式。如果Fq-子空间 ü={XqŤFX|XFqñ} 定义一个最大的分散线性集,然后我们称 FX索引为t的分散多项式。指数为t的分散多项式的渐近行为是一个有趣的开放问题。从这个意义上讲,索引为t的特殊分散多项式是那些UPG1个q[R无限数m。指数为0的异常零散单项多项式的分类q>5)和索引1在[1]中获得。在本文中,我们完成了索引为0的异常零散单项多项式的分类q4。同样,对于任意t,可以获得一些部分分类。结果,给出了索引为2的异常分散单项多项式的分类。

更新日期:2020-12-16
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