Approximate Odd Periodic Correlation Distributions of Binary Sequences (Special Issue on Spread Spectrum Techniques and Applications)

An approximate equation of the odd periodic correlation distribution for the family of binary sequences is derived from the exact even periodic correlation distribution. The distribution means the probabilities of correlation values which appear among all the phase-shifted sequences in the family. It is shown that the approximate distribution is almost the same as the computational result of some family such as the Gold sequences with low even periodic correlation magnitudes, or the Kasami sequences, the bent sequences with optimal even periodic correlation properties in the sense of the Welch's lower bound. It is also shown that the odd periodic correlation distribution of the family with optimal periodic correlation properties is not the Gaussian distribution, but that of the family of the Gold sequences with short period seems to be similar to the Gaussian distribution.