Some new classes of cyclic codes with three or six weights
Yongbo Xia Tor Helleseth Chunlei Li
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.
keywords: exponential sum weight distribution Cyclic code quadratic form.
A class of quaternary sequences with low correlation
Nian Li Xiaohu Tang Tor Helleseth
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.
keywords: Galois ring quaternary sequence quadratic form low correlation.

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