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Research Article | Open Access

The polycyclic codes over the finite field Fq

School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255049, China
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Abstract

This article extended the properties of the idempotent generator of cyclic codes to polycyclic codes over the finite field Fq. In addition, the check matrix of polycyclic codes was provided over Fq. Specifically, it has been proven that the constacyclic code is an MDS code over Fq if and only if its annihilator dual code is also an MDS code. Finally, we have provided some examples of good codes.

Keywords

polycyclic codesidempotent generatorcheck matrixMDS codes
CLC number: 94B15, 94B05

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 29707-29717
DOI: 10.3934/math.20241439

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Qi W. The polycyclic codes over the finite field Fq. AIMS Mathematics, 2024, 9(11): 29707-29717. https://doi.org/10.3934/math.20241439

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Received: 30 August 2024
Revised: 04 October 2024
Accepted: 14 October 2024
Published: 21 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)