Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation

Constructing a large family of p-ary sequences with large linear complexity and low correlation is very important for code division multiple access (CDMA) communication systems. By use of Klapper's method and d-form function, a large family S(r) of p-ary sequences with low correlation is constructed. Such family contains p2n sequences of period pn-1 with maximal nontrivial correlation value 4p(n)/(2)-1. The minimal and maximal linear complexity of the sequences family are proven to be 2(n)/(2)-2n and 3(n)/(2)-1×2(n)/(2)-2n for p > 5 and r=(pm-1-1)/(p-1), respectively. It is also proven that the maximal and minimal linearcomplexity of the sequences set are larger than 3(n)/(4)-1×2(n)/(4)-2n and 2(n)/(4)-2n for p=3, 5 and r=(pm-1-1)/(p-1), respectively. This sequences family can greatly improve the security of CDMA communication systems.