Abstract

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility of some polynomials in two indeterminates.

中文翻译：

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关于一类涉及迹图的置换有理函数

摘要

近年来，有限域上的置换有理函数引起了人们的高度兴趣。然而，其中只有少数被展出。本文研究了一类使用有限域扩展上的迹图构造的置换有理函数，特别是对于二次和三次扩展的情况。我们的成就是通过研究两个不定式中某些多项式的绝对不可约性而获得的。