本文選題：有限域　切入點：正規(guī)基　出處：《四川師范大學》2016年碩士論文

【摘要】：熟知,有限域上的正規(guī)基在計算機的軟件和硬件實現(xiàn)中都有廣泛的作用,尤其令人感興趣的是確定有限域上的高斯正規(guī)基,特別是高斯正規(guī)基的復雜度.本文第二章給出了有限域上一類(n,k)(k≥3)型高斯正規(guī)基的對偶基的復雜度的上下界,由此確定了有限域上(n,k)(k=1,2)型高斯正規(guī)基的對偶基的準確復雜度.進而完全確定了有限域上高斯正規(guī)基及其對偶基的乘法表和復雜度的對應關(guān)系.本文第三章給出了偶特征有限域上一類滿足特殊條件的高斯正規(guī)基的對偶基及其跡基的乘法表和復雜度,并證明了這類高斯正規(guī)基的跡正規(guī)基是最優(yōu)正規(guī)基.
[Abstract]:It is well known that the normal basis on a finite field plays a broad role in the software and hardware implementation of a computer, and it is of particular interest to determine the Gao Si normal base on a finite field. In the second chapter, we give the upper and lower bounds of the complexity of the dual bases of a class of Gao Si normal bases of type K 鈮，

本文編號：1671486