A class of quaternary sequences with low correlation

Nian  Li; Xiaohu  Tang; Tor Helleseth

doi:10.3934/amc.2015.9.199

Article Contents

2015, Volume 9, Issue 2: 199-210. Doi: 10.3934/amc.2015.9.199

This issue Previous Article Cyclic orbit codes and stabilizer subfields Next Article Binary codes from reflexive uniform subset graphs on $3$-sets

A class of quaternary sequences with low correlation

1.
Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, Sichuan 610031
2.
Department of Informatics, University of Bergen, N-5020 Bergen

Received: March 2014

Revised: November 2014

Published: May 2015

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Abstract

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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Mathematics Subject Classification: Primary: 94A05, 94A55.

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