A class of quaternary sequences with low correlation

A class of quaternary sequences $\mathbb{S}_{\lambda}$ had been proven to be optimal for some special values of $\lambda$. In this note, $\mathbb{S}_{\lambda}$ is investigated for all $\lambda$ by virtue of the $\mathbb{Z}_4$-valued quadratic forms over Galois rings. As a consequence, a new class of quaternary sequences with low correlation is obtained and the correlation distribution is also completely determined. It also turns out that the known optimal quaternary sequences $\mathbb{S}_{\lambda}$ for particular $\lambda$ can be easily obtained from our approach.