Códigos de cobertura em espaços de Hamming

Abstract

In this work, we will approach the issue to find the minimum cardinality of a covering code in the Hamming finite space. This minimum cardinality will be given by the function Kq(n, R), and we will introduce exact values and approximations to some classes of these functions through the covering codes theory. These constructions can be done through combinatory arguments and in some of them we will use algebraic tools using finite fields properties, the numbers addictive theory, constructions using matrixes. These constructions will be very useful to get upper bounds. on the other hand methods using the s-surjective and matrixes partition will be very useful to get some lower bounds to some classes of the function Kq(n, R)