Note sur la notion d'equivalence entre deux codes lineaires

AbstractIn this note, we consider the notion of simple components of a linear code over the field F and show that linear codes C and C′ are equivalent if and only if there exists an additive Hamming isometry f sending C onto C′ whose restriction to simple components of C are semi-linear. In case where F is of prime order, f is a linear map but in general f cannot always be taken to be globally semi-linear. We give an example where the restrictions of f to simple components must have different associated automorphisms