Some functional metrics in algebraic and combinatorial coding

Three approaches to coding problems can be systematically distinguished: probabilistic (essentially existential), algebraic, and combinatorial. This last approach searches for optimal configurations and relegates to the second order, the problems of complexity related to decoding. Enumeration, graphs, designs, and the extreme theory of groups are used. The optimization of a functional metric was used with the combinatorial approach in order to define the space considered and the distance. The codes then become particular groups of the metric space, which is defined by parameters such as length, number of words, and capacity for correction. Some of these parameters are imposed.