Constructing Gray maps from combinatorial geometries
PAŞA Abdullah YILDIZ · Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics · 2014
The focus of this work is constructing Gray maps for linear codes over a family of Frobenius rings, using tools from combinatorial geometries.The main combinatorial structure that are used are projective geometries P Gn(q), de…ned over Fq.Codes over Z p k , Galois rings, …nite chain rings and R k have been considered with respect to homogeneous weights.Using hyperplanes in projective geometries, distance preserving Gray maps from aforementioned rings to residue …elds have been constructed.The use of projective geometries serves as a novel approach to what was a primarily algebraic approach in the literature.The constructions also serve as a motivation for using homogeneous weights.