The geometric codes are the duals of the codes defined by the designs associated with finite geometries. The latter are generalized Reed-Muller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric constructions in the associated geometries, and the BCH bound from coding theory. Using Hamada’s formula, we ...

A code over GF(qm) can be imaged or expanded into a code over GF(q) using a basis for the extension field over the base field. The properties of such an image depend on the original code and the basis chosen for imaging. Problems relating the properties of a code and its image with respect to a basis have been of great interest in the field of coding theory. In this work, a generalized version ...

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new data. In order to overcome this drawback, we propose an algorithm aimed at learning both a dictionary and its dual: a linear mapping directly performing the ...