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Notice that if the probability of error on a [[discrete memoryless channel]] <math>p</math> is strictly less than one half, then ''minimum distance decoding'' is equivalent to ''maximum likelihood decoding'' since if
:<math>d(x,y) = d,\,</math>
then:
:<math>
\begin{
\mathbb{P}(y \mbox{ received} \mid x \mbox{ sent}) & {} = (1-p)^{n-d}p^d \\
& {} = (1-p)^n \left( \frac{p}{1-p}\right)^d \\
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