Hamming Distance between Codewords of Perfect Code

Theorem

Let $\KK$ be a $k$-perfect code.

The Hamming distance between codewords of $\KK$ may well be less than the maximum Hamming distance of $2 k + 1$.

Proof

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Also see

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

Sources

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