Abstract
Composing the Carlet map with the inverse Gray map, a new family of cyclic quaternary codes is constructed from 5-cyclic \(\mathbb{Z}_8 \)-codes. This new family of codes is inspired by the quaternary Shanbag–Kumar–Helleseth family, a recent improvement on the Delsarte–Goethals family. We conjecture that these \(\mathbb{Z}_4 \)-codes are not linear. As applications, we construct families of low-correlation quadriphase and biphase sequences.
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Zinoviev, D.V., Solé, P. Quaternary Codes and Biphase Sequences from \(\mathbb{Z}_8 \)-Codes. Problems of Information Transmission 40, 147–158 (2004). https://doi.org/10.1023/B:PRIT.0000043928.91210.68
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DOI: https://doi.org/10.1023/B:PRIT.0000043928.91210.68