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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
and
. Applying the triangle inequality, we have
(by our supposition).

But this contradicts the fact that **C**).
Let **C** be a -error correcting code. Then the spheres
S such that **c** **C** are mutually disjoint.

Bill Cherowitzo
2001-12-11