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COMPLEX WEIGHING MATRICES AND QUATERNARY CODES

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

Published online by Cambridge University Press:  22 October 2024

DANNI LU Open the ORCID record for DANNI LU [Opens in a new window] ,
MINJIA SHI Open the ORCID record for MINJIA SHI [Opens in a new window] ,
RONAN EGAN Open the ORCID record for RONAN EGAN [Opens in a new window]  and
PATRICK SOLÉ Open the ORCID record for PATRICK SOLÉ [Opens in a new window]
DANNI LU
Affiliation:
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei 230601, PR China e-mail: ludanni_in@163.com
MINJIA SHI*
Affiliation:
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei 230601, PR China
RONAN EGAN
Affiliation:
School of Mathematical Sciences, Dublin City University, Dublin, Ireland e-mail: ronan.egan@dcu.ie
PATRICK SOLÉ
Affiliation:
I2M, Aix Marseille Université, CNRS, Centrale Marseille, Marseilles, France e-mail: sole@enst.fr
*
e-mail: smjwcl.good@163.com
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Abstract

Weighing matrices with entries in the complex cubic and sextic roots of unity are employed to construct Hermitian self-dual codes and Hermitian linear complementary dual codes over the finite field $\mathrm {GF}(4).$ The parameters of these codes are explored for small matrix orders and weights.

Keywords

weighing matricesquaternary codesHermitian self-dual codesLCD codes

MSC classification

Primary: 05B20: Matrices (incidence, Hadamard, etc.)
Secondary: 94B05: Linear codes, general

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 112 , Issue 1 , August 2025 , pp. 14 - 22
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This research is supported in part by National Natural Science Foundation of China (12471490).

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