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.