A property of decomposable Golay codes which greatly simplifies sidelobe calculation

Abstract

Pure-sense complementary sequences are an important class of codes that were invented by Golay. With but two non-trivial exceptions, Golay codes of all known lengths are, or can be, made to be decomposable; that is, they can be considered to be formed from the apposition of two equal-length subcodes. Hence the technique in this letter applies to Golay codes of most known lengths. The value of the property is that it reduces the labor of computation of the autocorrelation function sidelobes of the Golay codes by a factor of at least two. Furthermore, it is applicable to either marine or manual calculation. It also provides another way of analyzing auto-correlation functions in general.