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The dynamics of permutations on irreducible polynomials
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2020-03-13 , DOI: 10.1016/j.ffa.2020.101664
Lucas Reis , Qiang Wang

We study degree preserving maps over the set of irreducible polynomials over a finite field. In particular, we show that every permutation of the set of irreducible polynomials of degree k over Fq is induced by an action from a permutation polynomial of Fqk with coefficients in Fq. The dynamics of these permutations of irreducible polynomials of degree k over Fq, such as fixed points and cycle lengths, are studied. As an application, we also generate irreducible polynomials of the same degree by an iterative method.



中文翻译:

不可约多项式置换的动力学

我们研究有限域上不可约多项式集合上的保度图。特别是,我们表明,集合度的不可约多项式的每一个排列ķFq 是由置换多项式的作用引起的 Fqķ 系数在 Fq。多项式k上不可约多项式的这些置换的动力学Fq,如固定点和循环长度,进行了研究。作为应用程序,我们还通过迭代方法生成了相同度数的不可约多项式。

更新日期:2020-03-13
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