New Construction of Pseudorandom Sequences with Optimal Autocorrelation

Abstract

In this paper, we present a general method to construct binary sequences of longer period with ideal autocorrelation property from a given binary sequence with ideal autocorrelation property. Furthermore, we show that if a given binary sequence with ideal autocorrelation property is described using the trace function, then it is explicitly extended to a binary sequence of longer period with ideal autocorrelation property in a trace representation. The GMW sequences are shown to be a natural extension of m-sequences with respect to this method. New binary sequences with ideal autocorrelation property are also explicitly constructed from known sequences of miscellaneous type by the method.