New Polyphase Sequence Families With Low Correlation Derived From the Weil Bound of Exponential Sums

In this paper, the sequence families of which maximum correlation is determined by the Weil bound of exponential sums are revisited. Using the same approach, two new constructions with large family sizes and low maximum correlation are given. The first construction is an analog of one recent result derived from the interleaved structure of Sidel´nikov sequences. For a prime p and an integer M|(p-1), the new M-ary sequence families of period p are obtained from irreducible quadratic polynomials and known power residue-based sequence families. The new sequence families increase family sizes of the known power residue-based sequence families, but keep the maximum correlation unchanged. In the second construction, the sequences derived from the Weil representation are generalized, where each new sequence is the elementwise product of a modulated Sidel´nikov sequence and a modulated trace sequence. For positive integers d <; p and M|(pn-1), the new family consists of (M-1)pnd sequences with period pn-1, alphabet size Mp, and the maximum correlation bounded by (d+1)√{pn}+3.