Weil Sequences: A Family Of Binary Sequences With Good Correlation Properties

We describe a family of binary sequences, called Wed sequences, which have prime length. The sequences are derived from the single quadratic-residue-based Legendre sequence using a "shift-and-add" construction. The Weil sequences have correlation sidelobes; bounded by 2 root p + 5, where p is the length. Thus they are asymptotically within a factor of two of the Welch bound. The sequences are optimally balanced when p is congruent to 3 modulo 4, and well-balanced otherwise. The family size is (p - 1)/2.