An Extension Of A Special Generalized Self-shrinking Sequence And Some Properties

In this paper, we expand the field of the special generalized self-shrinking sequence in [3]. In the other word, we build a special generalized self-shrinking sequence in GF(3) . They can be built as follows.Leta = (a₀,a₁,a₂,···)a m-sequence of degree n over GF(3). For each k = 0,1,2, ···, in case a_K = 0, we give up outputting; in case a_k = 1, we output a_k-1; in case a_k = 2, we output a_k-2 We can get the sequenceb = (b₀,b₁,b₂,···)It is called the sepecial generalized self-shrinking sequence in GF(3). It is easily seen that 2 · 3^n-1 is one of the periods of the sequence.In chapter 2, we find its important cryptography properties of the sequence by analysing its patterns. Some important conclusions as follows.Theorem 1 It is twenty-three that the number of 1-pattern 011··· 10 and 211 ··· 10 of length n — 5 in 2 ·3^n-1 continuous bits of b. So the least period of b is 2 · 3^n-1 .Theorem 2 For the sequence b, (?)k, 3 ≤ k ≤ n-5, it is 102·3^n-(k+5) that the number of 1-pattern of length k.Theorem 3 In one least period of b, we can find that the probability of 0,1,2 is equal, and it is 2 · 3^n-2 .Theorem 4 The linear complexity of b satisfy the inequality L(b) > 3^n-2.In chapter 3, we give several examples to proof some properties of our sequence.