On existence of 2-level autocorrelation sequences realized from the decimation-Hadamard transformation

We investigate the decimation-Hadamard transform (DHT) applied to 2-level autocorrelation sequences. We present the kth-order DHT by a matrix representation and show that odd order DHT cannot realize any 2-level autocorrelation sequences. We provide two interesting experimental results including one for the second-order DHT of the generalized GWM sequences.