On Some Special Normal Bases over Finite Fields
Qunying Liao · Journal of Sichuan University · 2005
Let q be a power of a prime p and n be a positive integer,K=F_q be the finit field with q elements and F=F_q~n be the n-th extension of K.If N={α_i｜i=0,1,0…,n-1}is a normal basis of F over F_q,B={β_i｜i=0,1,…,n-1}is the dual basis of N.Then the two sufficcient adn neccesary conditions for a,b∈F_q such that β=a+bα are given in this note.The author also gets the relationship between the mnltiplication tables of N and B.