On graphs and codes (Q1184492)

In a former paper the author showed how the binary Golay code can be obtained in a revealing way straight from the edge-graph of the icosahedron. This construction not only yields a basis for the code, but also supplies a simple description of all codewords. The author here shows that this construction is merely a special case of a general method of constructing codes from graphs. Codes with certain properties can be obtained by putting certain conditions on the graph. The author gives a construction of generating large numbers of self-dual codes. Some examples are described.