Lifting iso-dual algebraic geometry codes

In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field \(\mathbb {F}_{q}\) with q elements. Given a finite separable extension \(\mathcal {M}/\mathcal {F}\) of function fields and an iso-dual AG-code \(\mathcal {C}\) defined over \(\mathcal {F}\), we provide a general method to lift the code \(\mathcal {C}\) to another iso-dual AG-code \(\tilde{\mathcal {C}}\) defined over \(\mathcal {M}\) under some assumptions on the parity of the involved different exponents. We apply this method to lift iso-dual AG-codes over the rational function field to elementary abelian p-extensions, like the maximal function fields defined by the Hermitian, Suzuki, and one covered by the GGS function field. We also obtain long binary and ternary iso-dual AG-codes defined over cyclotomic extensions.