p^mq^n周期q元序列线性复杂度与k错复杂度的关系

A relationship between the linear complexity and the k-error linear complexity of q-ary sequences with periodp^mq^n

研究了q元周期序列线性复杂度和k错复杂度之间的关系,给出了k错复杂度严格小于线性复杂度的一个充要条件。当周期为N=pqn时,给出了使得LC(S+E)<LC(S)成立的错误多项式EN(x)的确切表达式,以及使得LCk(S)<LC(S)成立的最小的k值,即minerror(S)的值,结果表明minerror(S)与线性复杂度的重量密切相关;当周期为N=pmqn时,给出了使得LC(S+E)<LC(S)成立的用错误多项式EN(x)表达的一个充分条件。这里p为奇素数,q是素数且是一个模p2的本原根。

A relationship between the linear complexity and the terror linear complexity of periodic sequences over GF(q) is studied, A necessary and sufficient condition for which the terror linear complexity is strictly less than the linear complexity is showed. When the period N equals to pqn, an explicit expression of the error polynomial EN(x) for which LC(S+E)<LC(S) and the minimum value k for which LCk(S)<LC(S), i. e. minerror(S), are given. The results show that minerror(S) has a close relationship with the weight of the linear complexity. When the period N equals to pmqn, a sufficient condition expressed by the error polynomial EN(x) for which LC(S+E)<LC(S) is presented. Here p is an odd prime, and q is a prime and a primitive root (mod p2).