Some Classes Of Generalized Self-Shrinking Sequences On GF(3)

At first, this paper designs a new class of generalized self-shrinking sequences on GF(3), and the output model is:if ak=1, output ak-x, if ak=2, output ak-2+αk-1, or no output otherwise. It analyses the pseudorandomness of the class of generalized self-shrinking sequences, such as run distribution, least period and balance of symbols. It shows the correctness of the theorems which are about run distribution and least period by programs. The output model is quicker and easier and the run distribution is exacter than those in another classes of generalized self-shrinking sequences on GF(3)â'„â'…â'†. The run distribution is:if n≥8, in one least period, the number of 1-run whose length is 1 is:87·3n-6, the number of 2-run whose length is 1 is: 83-3n-6, and the range of the number of 0-run whose length is 1 is: 82-3n-6-24～82·3n-6+24; if 2≤k≤n-5, in one least period, the number of 1-run whose length is k is:60·3n-k-5. In accordance with the quick and easy output model and the good pseudorandomness of output sequences, this paper designs two another classes of generalized self-shrinking sequences on GF(3) whose character is combined output two adjacent digits in only one direction. The output model are:(1) if ak=1, output ak₁, if ak=2, output ak-1+ak, or no output otherwise, (2) if ak=1, output ak-2, if ak=2, output ak-1+ak, or no output otherwise. In the same way, it gives the pseudorandomness of the two classes of generalized self-shrinking sequences, such as run distribution, least period and balance of symbols. It gives the range of linear complexity of the three classes of generalized self-shrinking sequences when n=5,6,7 by special fast algorithm.