CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES.

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 PGn(q), defined over Fq. Codes over Zpk , Galois rings, finite chain rings and Rk have been considered with respect to homogeneous weights. Using hyperplanes in projective geometries, distance preserving Gray maps from aforementioned rings to residue fields 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. [ABSTRACT FROM AUTHOR]