A Model And Studying Of Self-shrinking Sequence With Modular Addition On M-sequence

A new self-shrinking model on GF(3) constructed with modular addition is presented. The upper bound of the period is3n, the lower bound is32[n/3]. The upper bound of the linear complexity is3n, the lower bound is32[n/3]-1. For the period and complexity of primitive trinomials and primitive quarternomials, the probability achieving better bound value are8/9,5/6. And deptly studied the run distributions,upper and lower bounds for the long-run value of k are given. It is shown that the new sequence has a huge period, a high linear complexity and good run distributions. Moreover, the model is extended to arbitrary finite field GF(q), and the sequence has a good cycle boundary values and linear complexity cutoffs.