A new family of binary pseudorandom sequences having optimal periodic correlation properties and larger linear span

A collection of families of binary {0,1} pseudorandom sequences is introduced. Each sequence within a family has period N=2"-1, where n=2m is an even integer. There are 2^m sequences within a family, and the maximum overall (nontrivial) auto- and cross-correlation values equals 2^m+1. Thus, these sequences are optimal with respect to the Welch bound on the maximum correlation value. Each family contains a Gordon-Mills-Welch (GMW) sequence, and the collection of families includes as a special case the small set of Kasami sequences. The linear span of these sequences varies within a family but is always greater than or equal to the linear span of the GMW sequence contained within the family. Exact closed-form expressions for the linear span of each sequence are given. The balance properties of such families are evaluated, and a count of the number of distinct families of given period N that can be constructed is provided