有限域子集上的Hermite判别法及推广

Hermite Criterion on subsets of finite fields and its generalization

利用有限生成代数的语言重述关于置换多项式的经典的Hermite判别法,并将其推广到有限城的子集上,另外也推广了其他一些关于有限域上置换多项式的结果,并给出了一定条件下相关函数的值集大小估计.最后,给出主要结果在有限域上n阶单位根群中的应用实例,并得到了一些有趣的结果.

The classical Hermite Criterion for permutation polynomials is rewritten via finite generated algebra, and generaliza tion of the criterion for subsets of finite fields is given. Moreover, generalizations of some other results about permutation poly nomials over finite fields are also given, and cardinality of value sets of the related function under specific conditions is esti mated. Finally, for a given finite field, some interesting results are obtained for the group of n - th roots of unity by the use of our main theorem.