Up: Basic Coding Topology for
For sake of contradiction, let's assume that there exist two distinct codewords c and c', both elements of C, and let's assume that there exists some vector v V, such that
. Applying the triangle inequality, we have
But this contradicts the fact that C).
(by our supposition).
Let C be a -error correcting code. Then the spheres
S such that c C are mutually disjoint.