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

A collection of families of binary {0,1} pseudorandom sequences (referred to as the families of No sequences) is introduced. Each sequence within a family has period N=2ⁿ-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 equal 2^m+1. Thus these sequences are optimum with respect to the Welch bound on the maximum correlation value. Each family contains a Gordon-Mils-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 is large. 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