A combinatorial construction of the Gray map over Galois rings
A Gray map is defined to be a weight preserving map from \(\mathbb{R}^n\) with the homogeneous weight to \(F^m\) with the Hamming weight where \(R\) is a ring and \(F\) is a field. Gray maps are an extremely important object of study in coding theory and are one of the reasons why codes over rings have become increasingly studied. The author gives an interesting new combinatorial construction of Gray maps when \(R\) is a Galois ring using affine hyperplanes in an associated affine geometry.
scientific article; zbMATH DE number 5569089
scientific article