Sequences with good randomness properties are quite important for stream ciphers. In this paper, a new class of quaternary sequences is constructed by using generalized cyclotomic classes of $\mathbb{Z}_{2p^m}$ $(m\geq1)$. The exact values of autocorrelation of these sequences are determined based on cyclotomic numbers of order $2$ with respect to $p^m$. Results show that the presented sequences have the autocorrelations with at most $4$ values.

翻译：具有良好随机性序列对流密码至关重要。本文利用$\mathbb{Z}_{2p^m}$ $(m\geq1)$上的广义分圆类构造了一类新型四元序列，并基于关于$p^m$的2阶分圆数确定了这些序列自相关函数的精确取值。结果表明，所构造序列的自相关值最多仅有4个不同取值。