Quaternary Sequences over Galois Rings with Good Correlation Obtained from Modified Binary Sequences over Galois Fields

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This research proposed the new sets of quaternary sequences over Galois rings obtained from modified some well-known sets of binary sequences over Galois fields, and clarified its correlation distributions to compare with those of the binary ones.First, we constructed the sets of quaternary sequences over Galois rings modified from the sets of binary sequences over Galois fields such as Gold Sequences and Gold-like sequences. Secondly, the correlation distributions were analyzed involving numerical computations. These quaternary sequences are easily built by the binary sequences without its characteristic polynomials over Galois rings. The correlation distributions of the new sets were clarified to be similar to those of the binary sequences we used. The nontrivial maximum correlation value in the sequence sets is approximately equal to √<2N>, where N represents the period of a sequence, which is optimal asymptotically according to the Welch Lower Bound, and the family size equal to those of the binary sequence sets. Thus, the results show that the proposed sets of quaternary sequences were able to apply to spread spectrum CDMA.