Abstract
A collection of families of binary {O,l} pseudorandom sequences (referred to as the families of No sequences) is introduced in this paper. Each sequence within a family has period N = 2- 1, where n = 2.m is an even integer. There are 2' sequences within a family and the maximum over all (nontrivial) auto and cross-correlation values equals 2+ 1. Thus these sequences are optimum 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 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 contructed also provided.
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