Open AccessJacobi forms over number fields from linear codes
Author(s) -
Boran Kim,
Chang Heon Kim,
Soonhak Kwon,
Yeong-Wook Kwon
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022459
Subject(s) - code (set theory) , mathematics , finite field , field (mathematics) , dual (grammatical number) , combinatorics , discrete mathematics , dual code , linear code , pure mathematics , computer science , algorithm , decoding methods , art , literature , set (abstract data type) , programming language , block code
We suggest a Jacobi form over a number field $ \Bbb Q(\sqrt 5, i) $; for obtaining this, we use a linear code $ C $ over $ R: = \Bbb F_4+u\Bbb F_4 $, where $ u^2 = 0 $. We introduce MacWilliams identities for both complete weight enumerator and symmetrized weight enumerator in higher genus $ g\ge 1 $ of a linear code over $ R $. Finally, we give invariants via a self-dual code of even length over $ R $.