The Model And Studying Of Multi-self-shrinking Sequences On Gf(3)

As an important kind sequence of pseudo-random sequences, Self-shrinking sequenceattracts extensive attention recently. In this paper,based on Self-shrinking sequence (reference[1]) and Multi-sclf-shrinking sequence (reference[3])over GF(2), the model of multi-self-shrinking sequence is reconstructed over GF(3). Its construction is as follows:Let a^∞=(a₀,a₁,a₂,….) be an m-sequence generated by an LFSR of length n overGF(3). We divide the bits of a^∞into the following groups:(a₀,a₁,a₂)(a₃,a₄,a₅)…(a_3k,a_3k+1,a_3k+2…If a3k=0, the bits of a^∞will be discarded; If a3k=1,a3k+1 is taken; If a3k=2, a3k+2 istaken,and also name the output-sequence z^∞=(z0,z1,z2,…) Multi-self-shrinking sequenceover GF(3).According to the theory of finite fields and run distribution, we discuss theperiod and linear complexity of MS S3- sequence and get some main conclusions:Conclusion 1 MSS3-scquencc z^∞is balanced and the period satisfies3^[n/3]-1＜L(z^∞)≤2×3^n-1;The linear complexity satisfies 3^[n/3]-1＜L(z^∞)≤2×3^n-1.Conclusion 2 Let f(x) be primitive trinomials or four-term polynomials of degree nover GF(3). a^∞is m-sequence generated by f(x), z^∞is a multi-selfshrunken maximumlength LFSR-sequence produced by a^∞,thenP(z^∞)≥2×3^[n/3],L(z^∞)＞2×3^[n/3]-1.In last part,we discuss some special cases of sequences based on general primitivepolynomials over GF(3)and give conjectures.</sub>