A New Class of Binary Sequence Family with Low Correlation and Large Linear Complexity

In this paper, we construct a class of (p(p + 2),p + 3,3p + 4) binary sequence family with low correlation and large linear complexity, where p and p + 2 are twin primes and p = 3 mod 4. This sequence family is generated by interleaving two Legendre sequences of period p and p+2, respectively. The balance properties of such family is evaluated, and for most cases the exact expressions for the linear complexity of each sequence are also given. The correlation property of our proposed sequence family is a little weak towards Welch bound, however, the linear complexity of each sequence is high, some of which can even reach p(p + 2).