Binary code imbalance and cyclic correlation sidelobes

The relationship between binary code imbalance and cyclic autocorrelation sidelobes is examined by extending results previously obtained for linear autocorrelation. Two measures of average sidelobe levels are discussed. One is the arithmetic mean of the signed sidelobes; the other is the root-mean-square of the average mean-square sidelobe, where the average is over codes having the same imbalance. These measures are important in choosing codes for an M-ary communication system that uses cyclic code shift keying (CCSK). We also provide a relationship between cyclic codes and Galois fields that identifies codes unsuitable for CCSK because their cyclic autocorrelation has at least one sidelobe equal to the magnitude of the peak.