Research on Periodic Correlation Bounds of Binary Sequence Pairs

The periodic correlation bounds of binary sequence pairs are derived. The definition of sequence pair and its autocorrelation and cross-correlation function are presented firstly. Then by using the weighting method the bounds of family size, length, maximum periodic autocorrelation sidelobe and mainlobe value, maximum periodic cross-correlation value are obtained. The previous binary sequences bounds, such as Sarwate and Welch bound can be considered as special cases of these bounds. These bounds present the theoretical foundation of designing binary sequence pairs set with good correlation properties.