On linear Z4-linear codes

In the paper “The Z₄-linearity of Kerdock, Preparata, Goethals and related codes”, written by A. Roger Hammons, P. Vijay Kumar, A.R. Calderbank, N.J.A. Sloane, Patrick Sole, 1993, the authors introduce the concept of a binary Z₄-linear code. This means a binary code, which-up to permutation of the coordinates-is the image of a linear code over the ring Z₄ under the so-called Gray map. Although the main aspect of Z₄-linearity is connected with nonlinear binary codes, it is also of interest to investigate the potential of the concept with respect to binary linear codes. In particular the structure of Z₄ -linear codes is given in the present paper