Relating propelinear and binary G-linear codes - Alves, MMS; Geronimo, JR; Palazzo, R.; Costa, SIR; Interlando, J. C.; Araujo, M. C. (Elsevier B.V., 2002)
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. (C) 2002 Elsevier B.V. B.V. All rights reserved.
Keywords: binary codes; Z(4)-linearity; propelinear codes; isometry groups; G-linearity