On the properties of Propelinear and G-linear codes

"The aim of this paper is to establish some of the structural properties which are common to the classes of binary translation-invariant propelinear codes and binary G-linear codes. In general, the codes in these classes are nonlinear codes, however they are part of the same symmetry n group decomposition Γ(Z_2^n) of Z_2^2 . We show that binary G-linear codes can be seen as translation-invariant propelinear codes. Finally, we establish a result which allows to identify when a code is a G-linear code."