Relating propelinear and binary G -linear codes

Abstract In this paper we establish the connections between two different extensions of Z 4 -linearity for binary Hamming spaces. We present both notions – propelinearity and G -linearity – in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G -linear codes are propelinear codes, and translation-invariant propelinear codes are G -linear codes.