Realizations from Decimation Hadamard transform for special classes of binary sequences with two-level autocorrelation

Abstract

In an effort to search for a new binary two-level autocorrelation sequence, the decimation-Hadamard transform (DHT) based on special classes of known binary sequences with two-level autocorrelation is investigated. In the second order DHT of a binary generalized Gordon-Mills-Welch (GMW) sequence, we show that there exist realizations which can be theoretically determined by the second order DHT in its subfield. Furthermore, we show that complete realizations of any binary two-level autocorrelation sequence with respect to a quadratic residue (QR) sequence by the second order DHT are theoretically determined. © Springer-Verlag Berlin Heidelberg 2006.