The Analysis Of New Types Of Bidirectional Linear Combination For Generalized Self-shrinkage Sequence Based On Mm-sequence In GF(3)

Considering that the linear combination coefficients in GF(3)can not be all 1,we use this linear combination model to further explore the properties of the sequence on the finite field.Compared with the previous ones,the new sequence is converted from bidirectional output to bidirectional linear combination output,and the combination coefficients cover GF(3)better.In this paper,the basic knowledge of cryptography,especially the runs'distribution of m-sequence and related contents of the mm-sequence are used to analyse the runs of constructed model sequence such as 1-run with length of 1,2-run of 1,0-run of 1,1-run of 2,2-run of 2,0-run of 2 and 1-run of k.So we are able to get to the upper and lower bounds of them and a lower bound of 0-run with length of k.What's more,we use a primitive polynomial to output the m-sequence with the help of Matlab.Then we modify it to be a mm-sequence by adding a 0 into one of the longest 0-run,checking the results with a special example.It turns out that the short runs occupy most of the the runs'distribution.The symbol distribution of 0,1 and 2 is balanced so the driving information will not be exposed to much.The period achieves the maximum value-2×3n-1,and the autocorrelation is also very well.