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==Syndrome decoding==
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'''Syndrome decoding''' is a highly efficient method of decoding a [[linear code]] over a ''noisy channel'' - i.e. one on which errors are made. In essence, syndrome decoding is ''minimum distance decoding'' using a reduced lookup table.
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
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