On a class of almost perfect sequences

Abstract

Periodic ±1 sequences all but one of whose out-of-phase autocorrelation coefficients are zero are studied by Wolfmann [9]. Using the equivalence of these almost perfect sequences to certain classes of cyclic divisible difference sets (as noted by Pott and Bradley [7]), we investigate the case θ = 2 (in the terminology of [9]). Sequences of periods 8, 12, and 28 are given and several nonexistence results are obtained. Our results suggest that it is unlikely to have such sequences for periods greater than 28. © 1997 Academic Press.