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 $.
Citation: Boran Kim, Chang Heon Kim, Soonhak Kwon, Yeong-Wook Kwon. Jacobi forms over number fields from linear codes[J]. AIMS Mathematics, 2022, 7(5): 8235-8249. doi: 10.3934/math.2022459
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 $.
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Boran Kim, Chang Heon Kim, Soonhak Kwon, Yeong-Wook Kwon. Jacobi forms over number fields from linear codes[J]. AIMS Mathematics, 2022, 7(5): 8235-8249. doi: 10.3934/math.2022459
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