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. Keywords Character sum, correlation, finite field, polyphase, sequence set

• Type: Journal
• Year: 2011
• Where: TIT
• Authors: Kai-Uwe Schmidt
• Keywords: Maximum Correlation, Sequence Family, Sequence Family Ωr, TIT 2011