New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case

• Published in: IEEE transactions on information theory Vol. 48; no. 11; pp. 2847 - 2867
• Main Author: Gong, Guang
• Format: Journal Article
• Language: English
• Published: IEEE 01.11.2002
• Subjects: Autocorrelation; Autocorrelation functions; Balancing; Binary sequences; Computer programs; Correlation; Cross correlation; Galois fields; Hardware; Optimization; Residues
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2002.804044

New designs for families of sequences over GF(p) with low cross correlation, balance property, and large linear span are presented. The key idea of the new designs is to use short p-ary sequences of period /spl upsi/ with the two-level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties. The resulting sequences are interleaved sequences of period /spl upsi//sup 2/. There are /spl upsi/ cyclically shift distinct sequences in each family. The maximal correlation value is 2/spl upsi/ + 3 which is optimal with respect to the Welch bound. Each sequence in the family is balanced and has large linear span. In particular, for binary case, cross/out-of-phase autocorrelation values belong to the set {1, -/spl upsi/, /spl upsi/ + 2, 2/spl upsi/ + 3, -2/spl upsi/ - 1}, any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span. It is shown that some families of these sequences can be implemented efficiently in both hardware and software.