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 | 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) × (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√p m +6 asymptotically achieves √2 times the equality of the Sidelnikov's lower bound when M = p m -1 for odd prime p.