异常分散多项式的分类研究

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-18 DOI:10.1016/j.jalgebra.2025.08.037

Daniele Bartoli , Massimo Giulietti , Giovanni Zini

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引用次数: 0

摘要

有限域上的散射多项式近年来受到越来越多的关注。其中一个原因是它们与最大秩距离码（MRD）有很深的联系。已知的异常分散多项式的分类结果，即分散在无限场扩展上的多项式，仅限于它们的指标r很小的情况，或大于多项式q度k的素数，或k为素数时小于k的整数。本文推广了Ferraguti和Micheli在2021年的研究结果，在r和k之间的最大值为奇数时，我们对异常散射多项式进行了完全分类，并给出了偶数时的部分结果。

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Towards the classification of exceptional scattered polynomials

Scattered polynomials over finite fields attracted an increasing attention in the last years. One of the reasons is their deep connection with Maximum Rank Distance (MRD) codes. Known classification results for exceptional scattered polynomials, i.e. polynomials which are scattered over infinite field extensions, are limited to the cases where their index ℓ is small, or a prime number larger than the q-degree k of the polynomial, or an integer smaller than k in the case where k is a prime. In this paper we completely classify exceptional scattered polynomials when the maximum between ℓ and k is odd, and give partial results when it is even, extending a result of Ferraguti and Micheli in 2021.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.