A Z(8)-linear lift of the binary Golay code and a nonlinear binary (96,2(37),24)-code
We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2(36), 24) code as the image of a Z(8)-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96, 2(37), 24) code. The tables in [2], and [12] show that this rode and some of its shortenings are better than the best (non)linear binary codes known so far. For instance, the best earlier known code of length 96 and minimum distance 24 had 2(33) words.
binary golay code gray isometry hensel lifting codes over rings homogeneous weight