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

From the algebraic properties on the family of the generalized self-shrinking sequences on GF(3), this paper proves that at least8/9sequences’s least period can achieve:2·3n-1on the family of the generalized self-shrinking sequences on GF(3). And it defines a new generalized self-shrinking sequences on GF(q) and proves that the family of generalized self-shrinking sequences on GF(q) not only constitute a commutative group but also constitute (q-1)n-dimensional linear space on GF(q),(q-1)-qn-1is the period of such sequences, and at least(q-1)/q sequences of the family of the generalized self-shrinking sequences on GF(q) have the least period:(q-1)·qn-1. The paper further proves that at least3n sequences with period of3n-1on the family of generalized self-shrinking sequences on GF(3). And over (q-1)/2·qn sequences with the period of (q-1)/2·qn-1on the family of generalized self-shrinking sequences on GF(q). At last, the lower bounds of linear complexity of generalized self-shrinking sequences on GF(3) and GF(q) are devived.