A theoretical study and computer search for binary sequences having specific auto-correlation functions

Abstract

Binary sequences find increasing use in electrical engineering applications of ranging, time measurement and communications. A property of interest in these applications is the autocorrelation function of the binary sequence or pair of sequences. Of the 2 possible sequences of length n, only a few have usable autocorrelation functions. There is, to date, no procedure known which will provide the sequence having a specific autocorrelation function, except for very particular cases . In this report, known properties of complementary sequences are reviewed. Almost complementary sequences are defined and the procedure to obtain them is outlined. A formula is derived for the number of different autocorrelation functions of the 2 possible sequences of length n bits. A computer search is implemented with the objective of discovering sequences with desirable autocorrelation functions.