1. Sequence Families With Low Correlation Derived From Multiplicative and Additive Characters.
- Author
-
Schmidt, Kai-Uwe
- Subjects
- *
MATHEMATICAL sequences , *STATISTICAL correlation , *FINITE fields , *MATHEMATICAL mappings , *CODE division multiple access , *SYNCHRONIZATION , *AUTOCORRELATION (Statistics) - Abstract
For integer r satisfying 0\leq r\leq p-2, a sequence family \Omega_r of polyphase sequences of prime period p, size (p-2)p^r, and maximum correlation at most 2+(r+1)\sqrtp is presented. The sequence families are nested, that is, \Omega_r is contained in \Omegar+1, which provides design flexibility with respect to family size and maximum correlation. The sequences in \Omega_r 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 \Omega_0, which was previously proposed by Scholtz and Welch. Sequence family \Omega_2 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF