GF(2)上周期为2p^n序列的m(s)

m(s) of Sequences with Period 2p^n over GF(2)

给出多项式的若干引理,并对引理进行证明。在此基础上,给出GF(2)上周期序列线性复杂度的表达形式,应用该表达式得出周期N=2pn的二元序列线性复杂度和m(s)之间的关系,其中p是个奇素数,并且2是一个模p2的本源根。结合魏算法,给出2个实例进行证明,结果表明该结果的正确性。

This paper gives some polynomial lemmas and proof of lemma. On basis of these lemmas, the expression of Linear Complexity（LC） of periodic sequences is gave. Application of the expression show the most important result of this article, a relationship between re（s） and the LC of a given sequence s with period N=2pn over GF（2）. Where p is an odd prime, 2 is a primitive root module p. Combined with Wei algorithm, it gives two examples to prove the results. Result shows that the relationship is correct.