Characterizing the autocorrelations of binary sequences

Abstract

The class of autocorrelation functions of binary sequences is studied in terms of their finite-dimensional projections; that is, the vector ranges of finite sets of consecutive correlation coefficients. These are convex polyhedra whose extreme points can be generated by binary sequences of bounded periods. Algorithms are given for the calculation of extreme points. Tables are presented for the extreme points and supporting hyperplanes of projections up to dimension five. Some conclusions about the general class of autocorrelations of binary sequences are drawn from these tables.