Autocorrelation of a Class of Quaternary Sequences of Period $2 p^{m}$

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{Z}_{2 p^{m}}(m \geq 1)$</tex>. The exact values of autocorrelation of these sequences are determined based on cyclotomic numbers of order 2 with respect to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p^{m}$</tex>. Results show that the presented sequences have the autocorrelations with at most 4 values.