Improved binary codes and sequence families from Z/sub 4/-linear codes

A bound on exponential sums over Galois rings is used to construct a nested chain of Z/sub 4/-linear binary codes and binary sequences. When compared with the chain of Delsarte-Goethals'(1975) codes, the codes in the new chain offer a larger minimum distance for the same code size. The binary sequence families constructed also make use of Nechaev's (1991) construction of a cyclic version of the Kerdock code. For a given value of maximum correlation, the binary sequences are shown to have a family size considerably larger than the best sequence families known.