  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.
