Covering and regular distance graphs

One of the technical aspects which is key in Telecommunications is linked with the use of error correcting codes for the transmission of the information. Nowadays, and actually, a very simple kind of code is used; the physical implementation of an error correcting code is complicated and expensive. In the field of Theoretical Computer Science they are trying to tackle the problem of error correcting codes from many different angles. One of these is the Algebraic Combinatorics Theory and, in particular, the Distance-Regular Graphs, from which good codes may be constructed. This paper presents the most important topics of the Distance-Regular Graph Theory which are needed to construct the covering •Åα:(Z/2)ⁿ⇒¦). It also constructs this covering and generalizes the results in the sense of clarifying that • is also a e-covering, e≥3. The last result will be a key in the study of algebraic properties of Completely-Regular Codes associated to Distance-Regular Graphs.