Large families of quaternary sequences with low correlation

Abstract

A family of quaternary (Z/sub 4/-alphabet) sequences of length L=2/sup r/-1, size M/spl ges/L/sup 2/+3L+2, and maximum nontrivial correlation parameter C/sub max//spl les/2/spl radic/(L+1)+1 is presented. The sequence family always contains the four-phase family /spl Ascr/. When r is odd, it includes the family of binary Gold sequences. The sequence family is easily generated using two shift registers, one binary, the other quaternary. The distribution of correlation values is provided. The construction can be extended to produce a chain of sequence families, with each family in the chain containing the preceding family. This gives the design flexibility with respect to the number of intermittent users that can be supported, in a code-division multiple-access cellular radio system. When r is odd, the sequence families in the chain correspond to shortened Z/sub 4/-linear versions of the Delsarte-Goethals codes.