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Degree of orthomorphism polynomials over finite fields
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-07-02 , DOI: 10.1016/j.ffa.2021.101893 Jack Allsop 1 , Ian M. Wanless 1
中文翻译:
有限域上的正态多项式的次数
更新日期:2021-07-02
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-07-02 , DOI: 10.1016/j.ffa.2021.101893 Jack Allsop 1 , Ian M. Wanless 1
Affiliation
An orthomorphism over a finite field is a permutation such that the map is also a permutation of . The degree of an orthomorphism of , that is, the degree of the associated reduced permutation polynomial, is known to be at most . We show that this upper bound is achieved for all prime powers . We do this by finding two orthomorphisms in each field that differ on only three elements of their domain. Such orthomorphisms can be used to construct 3-homogeneous Latin bitrades.
中文翻译:
有限域上的正态多项式的次数
有限域上的同构 是一个排列 使得地图 也是一个排列 . 该程度的正形的,即相关联的约简置换多项式的次数,已知至多为 . 我们证明了所有素数都达到了这个上限. 我们通过在每个域中找到两个正同态来做到这一点,它们仅在其域的三个元素上有所不同。这种正态可以用来构造 3-homogeneous Latin bitrades。