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Suppose that <math>C\subset \mathbb{F}_2^n</math> is a linear code of length <math>n</math> and minimum distance <math>d</math> with [[parity-check matrix]] <math>H</math>. Then clearly <math>C</math> is capable of correcting up to
:<math>t = \left\lfloor\frac{d-1}{2}\right\rfloor</math>
errors made by the channel (since if no more than <math>t</math> errors are made then minimum distance decoding will still correctly decode the incorrectly transmitted codeword).
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Notice that this will always give a unique (but not necessarily accurate) decoding result since
: <math>Hx = Hy</math>
if and only if <math>x=y</math>. This is because the parity check matrix <math>H</math> is a generator matrix for the dual code <math>C^\perp</math> and hence is of full [[rank (linear algebra)|rank]].
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