Matrix representations of aperiodic auto and cross correlation functions

Abstract

The matrix representations of aperiodic auto- and cross-correlation functions are useful in revealing new properties of correlation functions. The “shared autocorrelation function property” related to nonstandard PSK Golay sequences previously observed through computer search only are shown to propagate to infinite sequence lengths. The additivity property for mod-H codeword sequences and the aperiodic autocorrelation function matrices of phase shift keying (H-PSK) sequences is also discussed. This shows that sequences with specific autocorrelation functions are more naturally described using the codeword sequences, in agreement with Davis and Jedwab's discovery that a large collection of PSK Golay complementary sequences can be concisely described as Reed Muller codewords.