【摘要】 提出了在特征为p的有限域上 ,周期为N =npv(p为素数 ,且gcd(n ,p) =1)的序列的线性复杂度可由 ( 1- xN)的不可约分解中因子的次数及在sN(x) (以序列的前N个数字作为系数而构成的多项式 )中的重数来确定 ,讨论了Hasse导数与序列的线性复杂度的关系 ,在此基础之上 ,给出了Games Chan算法的另外一种推导 .更多还原

【Abstract】 This paper presents that the linear complexity of an N-periodic sequence with components in a finite field of characteristic p with N= npv, where p is a prime and gcd(n, p)=1, is determined in terms of the degrees of the irreducible factors of 1-xN and their multiplicities as factors of the polynomial sN(x) whose coefficients are the first N digits of the sequence. The relation between the Hasse derivative and the linear complexity of periodic sequence is discussed, on the basis of which another proof of the Games-Chan algorithm is given.更多还原