The Research On Linear Complexity Distributing Of Periodic Sequences

When we design the keystreams of cipher streams,the linear complexity and k-e rror com-plexity of sequences as two crucial pointers play an important role in deciding the quality of keystreams. The scholars from all over the world come to research them in deep.the experts of China Ding and Xiao etc advanced the steady theory of cipher streams,people begin to research k-error linear complexity in a deep-going way,Stamp and Martin,K.Kurosawa,Kaida etc obtained very good results. Schlars of abroad Niederreiter and Meidl carry through a pioneering study of stat istics properties of the linear complexity and k-error complexity random sequences. this arti-cle sums up the results of recent years relating to linear complexity,and uses the Discrete Fourier Transform to get the distributing of its complexity and the bounds of expected k-error linear com-plexity,this article gives some extend prove of Meidl’s theorem.and finds a more compact bound about k error linear complexity. and discuss the k-error linear complexity distributing when k=1,2of p" periodic sequence on Fp,and obtain several properties and conclusions.