Jacobi forms over number fields from linear codes

초록

We suggest a Jacobi form over a number field Q(root 5, i); for obtaining this, we use a linear code C over R := F-4 + uF(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.

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