201310.3202v2 New Identities Relating Wild Goppa Codes

For a given support L∈F n q m and a polynomial g∈F q m [x] with no roots in F q m , we prove equality between the q -ary Goppa codes Γ q (L,N(g))=Γ q (L,N(g)/g) where N(g) denotes the norm of g , that is g q m−1 +⋯+q+1 . In particular, for m=2 , that is, for a quadratic extension, we get Γ q (L,g q )=Γ q (L..