A New Model And Studying Of Self-shrinking Sequence Developed On Gf(q)

Self-shrinking sequence is an important kind of pseudo-random sequences. Period and linear complexity are classic measures of pseudo-random sequences. So, it becomes an important issue to construct new models of Self-shrinking sequence that could generate sequences with great period and high linear complexity. In view of this question, a new model of Self-shrinking sequence over is constructed. After the study of the period and linear complexity of the generated sequence using the theory of finite fields, there are some main conclusions :The upper bound of the period is 3ⁿ, the lower bound is 3^2(?)n/3(?) ;The upper bound of linear complexity is 3ⁿ, the lower bound is 3^2(?)n/3(?)-1 ; Moreover, the period and linear complexity of the generated sequence based on primitive trinomials and quarternomials of degree n over are discussed. And the model is extended to arbitrary finite field GF(q). Obtain these conclusions :the upper bound of the period of the generated sequences is (qⁿ(q-1))/2 the lower bound is q^{(q-1)(?)n/q(?)}; The upper bound of linear complexity of the generated sequences is (qⁿ(q-1))/2 , the lower bound is q^{(q-1)(?)n/q(?)-1}...