A family of binary (t,t-1)-QF sequences with high linear spans and good correlation functions

Binary sequences with large linear spans and good correlation functions have many important applications in spread spectrum communications and security. In this paper, we constructed a family of binary sequences called (t,t-1)-QF sequences, which is determined by quadratic forms of the finite field GF(qⁿ) over GF(q). The size of the family, the periods, correlation functions and linear spans of (t,t-1)-QF sequences are also calculated. Therefore, the family of (t,t-1)-QF sequences can be a candidate for utilization in spread spectrum communications and cryptography