求GF(pm)上周期为kn的序列线性复杂度的快速算法

提出和证明了求GF(p^m)上周期为kn的序列线性复杂度和极小多项式的一个快速算法， 其中p是素数， gcd(n， p^m-1)=1且p^m-1=kt， n，k与t均为正整数．该算法推广了陈豪提出的求GF(p^m)上周期为3n的序列线性复杂度的一个快速算法， 其中p是素数， gcd(n， p^m-1)=1且p-1=3t， n与t均为正整数．结合一些已知的快速算法， 可以快速计算GF(p^m)上周期为kn的序列线性复杂度， 最后给出一个具体例子．

Fast algorithm for determining the linear complexity of sequences over GF(p~m) with the period kn

A fast algorithm is presented for determining the linear complexity and the minimal polynomial of sequences over GF(pm) with the period kn,where p is a prime,gcd(n,pm-1)=1,pm-1=kt,and n,k and t are integers.The algorithm presented here covers the algorithm proposed by Chen Hao for determining the linear complexity of sequences over GF(pm) with the period 3n,where p is a prime,gcd(n,pm-1)=1,p-1=3t,and n and t are integers.Combining the proposed algorithm with some known algorithms,the linear complexity of se...