Abstract: A new family of p-phase highest coordinate sequences, is constructed by using the highest coordinate of the generalized Kerdock codes over the ring . This paper not only deduces an exact formula on the linear complexities of the sequences, but also derives an estimate of the correlation of the sequences by utilizing the Weil exponential sums over Galois rings. Results shows that these sequences have both large linear complexities and low crosscorrelation and nontrivial autocorrelation, which make it possible to be the code sequences in CDMA communication systems.

Key words: Galois ring, highest coordinate sequence, linear complexities, correlation

摘要： 利用环 上广义Kerdock码的最高权位生成了一类p元最高权位序列，并对其密码特性进行研究。给出序列线性复杂度的准确计算公式，利用Galois环上的Weil指数和估计对序列的互相关性及非同步自相关性进行刻画。实验结果表明，构造的最高权位序列具有大的线性复杂度和极低的互相关性及非同步自相关性，可作为CDMA通信系统中的码序列。

关键词: Galois环, 最高权位序列, 线性复杂度, 相关性

CLC Number: 

• TP309