The Reserch Of Least Periods Of Generalized Self-shrinking Sequences On GF(q)

According to the generalized self-shrinking sequence family based on the m-Sequence on GF(3), using the new algebraic method proves that (3n-1)/3n sequence acheive:2·3n-1on GF(3).Accordingly given sequence can not achieve the least period of concrete form and spread the conclusion to GF(q),we prove that (?) sequences’s least period can achieve:(q-1)·qn-1.Finally,this paper analyse the linear complexity and balance of the generalized self-shrinking sequence family on GF(3) and GF(q) and Present the upper bound of the linear complexity, lower bound which is good result.