Upper Bound of Hamming Distance for Length of K-Error-Correcting Code

Theorem

Let $C$ be an error-correcting code whose Hamming distance is no less than $2 k + 1$ for some $k \in \N$.

Then $C$ is $k$-error-correcting.

Proof

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Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): error-correcting code