Lifting iso-dual algebraic geometry codes

Abstract

In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field 𝔽q with q elements. Given a finite separable extension M/F of function fields and an iso-dual AG-code C defined over F, we provide a general method to lift the code C to another iso-dual AG-code C´ defined over 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.