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

本文提出了一组新的伽罗瓦环上的四元序列，这些四元序列是在对伽罗瓦场上一些已知的二元序列进行修正的基础上得到的，并澄清了它们的相关分布，以便与二元序列的相关分布进行比较。首先，我们从伽罗瓦域上的二值序列集（如Gold序列和Gold-like序列）出发，构造了伽罗瓦环上的四元序列集。其次，通过数值计算分析了相关分布。这些四元序列可以很容易地由伽罗瓦环上没有特征多项式的二元序列构造而成。新集合的相关分布与我们使用的二值序列相似。序列集的非平凡最大相关值近似等于√<2N>，其中N表示序列的周期，根据Welch下界是渐近最优的，族大小等于二值序列集的族大小。结果表明，所提出的四元序列集能够应用于扩频CDMA。

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.