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Research Article | Open Access

Jacobi forms over number fields from linear codes

Boran Kim1( ), Chang Heon Kim2, Soonhak Kwon2, Yeong-Wook Kwon3
Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Korea
Department of Mathematics, Sungkyunkwan University, Seobu-ro, Suwon 16419, Korea
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Korea
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Abstract

We suggest a Jacobi form over a number field Q ( 5 , i ); for obtaining this, we use a linear code C over R := F 4 + u F 4 , where u 2 = 0. We introduce MacWilliams identities for both complete weight enumerator and symmetrized weight enumerator in higher genus g ≥ 1 of a linear code over R. Finally, we give invariants via a self-dual code of even length over R.

Keywords

Jacobi formFrobenius ringlinear codeself-dual codeinvariant
CLC number: 11F50, 94B05, 05E99

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8235-8249
DOI: 10.3934/math.2022459

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Cite this article:
Kim B, Kim CH, Kwon S, et al. Jacobi forms over number fields from linear codes. AIMS Mathematics, 2022, 7(5): 8235-8249. https://doi.org/10.3934/math.2022459

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Received: 23 November 2021
Revised: 06 February 2022
Accepted: 13 February 2022
Published: 15 May 2022
©2022 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)