On binary sequences of period n = p(m)-1 with optimal autocorrelation

Abstract

Binary sequences of period n = p(m) - 1 for an odd prime p are introduced in [4] by taking the characteristic sequence of the image set of the polynomial (z + 1)(d) + az(d) + b over the finite field F,- of p(m) elements. It was shown in [4] that they are (almost) balanced and have optimal autocorrelation in the case where the polynomial can be transformed into the form z(2) - C. In this paper, we show that the sequences are (almost) balanced and have optimal autocorrelation in the case of d = (p(m) + 1)/2, a = (-1)(d-1) and b = +/-1. Furthermore, we show that they are equivalent to the Lempel-Cohn-Eastman sequence in [2] in the balanced case. We also give a direct proof of the autocorrelation property of the Lempel-Cohn-Eastman sequence and discuss its linear complexity.