有限域上的互反正规基及其乘法表  

Normal Basis and Its Inverse and Their Multiplication Tables Over Finite Fields

作　　者：苏丹丹[1] 付萍 

机构地区：[1]罗定职业技术学院教育系,广东罗定527200 [2]北京市昌平区回龙观中学,北京昌平102200

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2014年第4期408-412,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金重大项目(10990011)

摘　　要：设q为素数的方幂,n为正整数,Fqn为有限域Fq的n次扩域,N={ξ,ξq,…,ξqn-1}和B={ξ-1,ξ-q,…,ξ-qn-1}为Fqn在Fq上的互反正规基.证明了互反正规基存在的4个充分条件,并给出判断互反正规基存在性的程序设计,以及对偶互反正规基乘法表的一个刻画和下界,最后得出存在互反本原最优正规基的充要条件.Let q be a power of a prime and n be a positive integer,Fqbe the finite field with q elements,Fqnthe n-th extension of Fq.Suppose that N={ξ,ξq,…,ξq^n-1}and B={ξ^-1,ξ^-q,…,ξ^-qn-1}are normal bases and its inverse of Fqnover Fq.In this paper,the authors prove the following main results：（1）Four sufficient conditions are obtained and a program is designed to determine some nfor which finite fields exist normal basis and its inverse;（2）The multiplication tables of dual inverse normal bases are characterized,and the lower bounds of complexity of multiplication tables are obtained;（3）The sufficient and necessary conditions are given which finite fields exist primitive inverse optimal normal bases.

关 键 词：有限域 互反 正规基 对偶基 最优 乘法表 

分 类 号：O156.1[理学—数学]