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NEW OPTIMAL LINEAR CODES OVER $\ \boldsymbol {\mathbb {Z}_{4}}$

Part of: Theory of error-correcting codes and error-detecting codes

Published online by Cambridge University Press:  03 June 2022

HOPEIN CHRISTOFEN TANG Open the ORCID record for HOPEIN CHRISTOFEN TANG [Opens in a new window]  and
DJOKO SUPRIJANTO Open the ORCID record for DJOKO SUPRIJANTO [Opens in a new window]
HOPEIN CHRISTOFEN TANG
Affiliation:
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia e-mail: [email protected]
DJOKO SUPRIJANTO*
Affiliation:
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
*
e-mail: [email protected]
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Abstract

We present novel approaches for constructing linear codes over $\mathbb {Z}_{4}$ from the known ones. We obtain new linear codes, many of which are optimal. In particular, we find all optimal codes of type $4^{k_{1}}2^{k_{2}}$ for $k_{1}=2,~k_{2}=0$ and many optimal codes for $k_{1}=3,~k_{2}=0.$

Keywords

ℤ 4-linear codesPlotkin boundoptimal codes

MSC classification

Primary: 94B05: Linear codes, general
Secondary: 94B65: Bounds on codes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 1 , February 2023 , pp. 158 - 169
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This research is supported by Institut Teknologi Bandung (ITB) and the Ministry of Education, Culture, Research and Technology (Kementerian Pendidikan, Kebudayaan, Riset dan Teknologi (Kemdikbud-ristek)), Republic of Indonesia.

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