On the cross-correlation distributions between p-ary m-sequences and their decimated sequences

For the past decades, maximal linear recursive sequences (m-sequences) have been studied by many researchers. M-sequences have ideal autocorrelation property, which is useful in various wireless communication systems. Some m-sequences have low cross-correlation values which is essential property for extensive application of code division multiple access (CDMA) of spread spectrum communication systems for multiple users. What is involved in study of m-sequences is to evaluate explicitly the values of the cross-correlation function between p-ary m-sequences and their decimated m-sequences by the decimation factor d. Generally, it is difficult to evaluate the distributions of cross-correlation values. However, when the decimation value d takes on some special values, the explicit evaluation of the cross-correlation function is possible. In this paper, we review the cross-correlation distributions of p-ary msequences and their decimated m-sequences for various d.