New Construction of M-Ary Sequence Families With Low Correlation From the Structure of Sidelnikov Sequences

For prime p and a positive integer m, it is shown that M-ary Sidelnikov sequences of period p(2m) - 1, if M vertical bar p(m) - 1, can be equivalently generated by the operation of elements in a finite field GF(p(m)), including a p(m)-ary m-sequence. From the (p(m) - 1) x (p(m) + 1) array structure of the sequences, it is then found that a half of the column sequences and their constant multiples have low correlation enough to construct new M-ary sequence families of period p(m) - 1. In particular, new M-ary sequence families of period p(m) - 1 are constructed from the combination of the column sequence families and known Sidelnikov-based sequence families, where the new families have larger family sizes than the known ones with the same maximum correlation magnitudes. Finally, it is shown that the new M-ary sequence family of period p(m) - 1 and the maximum correlation magnitude 2 root p(m) + 6 asymptotically achieves root 2 times the equality of the Sidelnikov's lower bound when M = p(m) - 1 for odd prime p.