On the correlation distribution of Delsarte-Goethals sequences

For odd integer m ≥ 3 and t = 0, 1, . . . , m−1 2 , we define Family V (t) to be a set of size 2m(t+1) containing binary sequences of period 2m+1 − 2. The nontrivial correlations between sequences in Family V (t) are bounded in magnitude by 2+2(m+1)/2+t . Families V (0) and V (1) compare favourably to the small and large Kasami sets, respectively. So far, the correlation distribution of Family V (t) is only known for t = 0. A general framework for computing the correlation distribution of Family V (t) is established. The correlation distribution of V (1) is derived, and a way to obtain the correlation distribution of V (2) is described. Keywords Galois ring, Low correlation, Quadratic Form, Sequence Set

• Type: Journal
• Year: 2011
• Where: DCC
• Authors: Kai-Uwe Schmidt
• Keywords: Computer Graphics, Correlation Distribution, DCC 2011, Large Kasami Sets, Nontrivial Correlations