New non-linear families of code-sequences with correlation properties better than linear families

The performance of direct-sequence code-division multiple-access systems depends on the correlation properties of the used code-sequences. In this paper, the peak and average correlation properties of binary families derived from `Z4-linear´ families of quadriphase sequences are compared to the results for well-known `linear´ families. It is shown that these families have remarkably better periodic peak correlation parameters than `linear´ families but an improvement of the average mean-square correlation properties has not been found. For increasing length, the average interference parameter tends to the expected value of the interference parameter for random sequences. Therefore, in this paper, a construction method based on linear optimization is described which results in families with low average interference parameters