Shared Autocorrelation Property of Sequences

Due to the low Peak-to-Mean Envelope Power Ratio (PMEPR) of Golay sequences together with their connection to generalized Reed-Muller codes, many authors have proposed using Golay sequences as codewords in orthogonal frequency-Division Multiplexing (OFDM). Golay sequences that unexpectedly share the same aperiodic autocorrelation function can be used to construct longer Golay sequences. The authors study the shared autocorrelation property of general sequences with the ultimate goal of using those results to find other low power sequences. In this paper, they provide several new constructions of families of pairs of sequences with the shared autocorrelation property that enable one to explain nearly all of the binary shared autocorrelation property for sequences of lengths up to 24.