Twisting geometric codes

The aim of this paper is to explain how, starting from a Goppa code C(X,G,P1,…,Pn) and a cyclic covering π:Y→X of degree m, one can twist the initial code to another one C(X,G+Dχ,P1,…,Pn), where Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y/X), in the hope that ℓX(G+Dχ)>ℓX(G). We give, using a MAGMA program, several examples where this occurs, and where both the initial and twisted codes have same minimum distance, so that initial codes have been improved.