A Class of Balanced Binary Sequences with Optimal Autocorrelation Properties

Abstract

The construction of a class of balanced binary sequences with optimal autocorrelation properties is described. Given any odd prime p and any positive integer m, a balanced (±1) binary sequence of length pm − 1 whose cyclic autocorrelation function c(τ) satisfies c(0) = pm − 1, and, for τ ≠ 0, c(τ) = +2 or −2 when (pm − 1)/2 is odd, and c(τ) = 0 or −4 when (pm − 1)/2 is even is constructed. Optimality is proved by showing that every balanced binary sequence has at least two distinct out-of-phase correlation values which are at least as large as those obtained here. © 1977, IEEE. All rights reserved.