Sequence Families With Low Correlation Derived From Multiplicative and Additive Characters
Kai‐Uwe Schmidt · IEEE Transactions on Information Theory · 2011
For integerrsatisfying 0 ≤r≤p-2, a sequence family Ωrof polyphase sequences of prime periodp, size (p-2)pr, and maximum correlation at most 2 +(r+1) √(p)is presented. The sequence families are nested, that is, Ωris contained in Ωr+ 1, which provides design flexibility with respect to family size and maximum correlation. The sequences in Ωrare 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 Ω2is 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.