Jacobi forms over number fields from linear codes

Boran Kim; Chang Heon Kim; Soonhak Kwon; Yeong Wook Kwon

doi:10.3934/math.2022459

Jacobi forms over number fields from linear codes

Boran Kim, Chang Heon Kim, Soonhak Kwon, Yeong Wook Kwon

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We suggest a Jacobi form over a number field Q(√5; i); for obtaining this, we use a linear code C over R:= F₄ + uF₄, where u² = 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.

Original language	English
Pages (from-to)	8235-8249
Number of pages	15
Journal	AIMS Mathematics
Volume	7
Issue number	5
DOIs	https://doi.org/10.3934/math.2022459
State	Published - 2022

Keywords

Frobenius ring
Invariant
Jacobi form
Linear code
Self-dual code

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10.3934/math.2022459

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title = "Jacobi forms over number fields from linear codes",

abstract = "We suggest a Jacobi form over a number field Q(√5; i); for obtaining this, we use a linear code C over R:= F4 + uF4, where u2 = 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 = "Frobenius ring, Invariant, Jacobi form, Linear code, Self-dual code",

author = "Boran Kim and Kim, {Chang Heon} and Soonhak Kwon and Kwon, {Yeong Wook}",

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year = "2022",

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language = "English",

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T1 - Jacobi forms over number fields from linear codes

AU - Kim, Boran

AU - Kim, Chang Heon

AU - Kwon, Soonhak

AU - Kwon, Yeong Wook

PY - 2022

Y1 - 2022

N2 - We suggest a Jacobi form over a number field Q(√5; i); for obtaining this, we use a linear code C over R:= F4 + uF4, where u2 = 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.

AB - We suggest a Jacobi form over a number field Q(√5; i); for obtaining this, we use a linear code C over R:= F4 + uF4, where u2 = 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.

KW - Frobenius ring

KW - Invariant

KW - Jacobi form

KW - Linear code

KW - Self-dual code

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U2 - 10.3934/math.2022459

DO - 10.3934/math.2022459

M3 - Article

AN - SCOPUS:85129863329

SN - 2473-6988

VL - 7

SP - 8235

EP - 8249

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 5

ER -

Jacobi forms over number fields from linear codes

Abstract

Keywords

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