TABLE OF CONTENTS In this chapter, we introduce cyclic difference sets and their relationship to binary sequences with 2-level autocorrelation. In terms of this relation, we exhibit the balance, constant-on-cosets, and 2-tuple balance property of binary sequences with 2-level autocorrelation and derive some constraints on their Fourier spectra and an achievable upper bound for the linear span of binary 2-level autocorrelation sequences.
A cyclic difference set modulo v, also called a cyclic ( v, k, ?) difference set, is a set D = { d 1 , d 2, , d k} of k integers distinct modulo v, such that the congruence d i d j ? t (mod v) has exactly ? solution pairs ( d i , d j) of elements of D, for each integer t, 1 ? t ? v 1 .
Note. Since there are k( k 1) choices of d i ? d j from D, giving each of v 1 values of t exactly ? times, we have k( k 1) = ?( v 1) as a necessary condition for a cyclic ( v, k, ?) difference set to exist.
D = {0, 1, 2, 4} is a cyclic (7, 4, 2) difference set, as...
