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AMC

In this paper, a class of three-weight cyclic codes over prime fields $\mathbb{F}_p$ of odd order whose
duals have two zeros, and a class of six-weight cyclic codes whose
duals have three zeros are presented. The
weight distributions of these cyclic codes are derived.

AMC

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.

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