Jacobi forms over number fields from linear codes

Abstract

<abstract><p>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 $.</p></abstract>