Sequence Families With Low Correlation Derived From Multiplicative and Additive Characters

For integer r satisfying 0 ≤ r ≤ p-2, a sequence family Ωr of polyphase sequences of prime period p, size (p-2)pr, and maximum correlation at most 2 +(r+1) √(p) is presented. The sequence families are nested, that is, Ωr is contained in Ωr + 1, which provides design flexibility with respect to family size and maximum correlation. The sequences in Ωr are derived from a combination of multiplicative and additive characters of a prime field. Estimates on hybrid character sums are then used to bound the maximum correlation. This construction generalizes Ω₀, which was previously proposed by Scholtz and Welch. Sequence family Ω₂ is closely related to a recent design by Wang and Gong, who bounded its maximum correlation using methods from representation theory and asked for a more direct proof of this bound. Such a proof is given here and an improvement of the bound is provided.