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A code ''C'' whose parameters satisfy ''k'' +''d'' = ''n'' + 1 is called '''maximum distance separable''' or '''MDS'''. Such codes, when they exist, are in some sense best possible.
If ''C''<sub>1</sub> and ''C''<sub>2</sub> are two codes of length ''n'' and if there is a permutation ''p'' in the [[symmetric group]] ''S''<sub>''n''</sub> for which (''c''<sub>1</sub>,...,''c''<sub>''n''</sub>) in ''C''<sub>1</sub> if and only if (''c''<sub>''p''(1)</sub>,...,''c''<sub>''p''(''n'')</sub>) in ''C''<sub>2</sub>, then we say ''C''<sub>1</sub> and ''C''<sub>2</sub> are '''permutation equivalent'''. In more generality, if there is an <math>n\times n</math> [[monomial matrix]] <math>M\colon \mathbb{F}_q^n \to \mathbb{F}_q^n</math> which sends ''C''<sub>1</sub> isomorphically to ''C''<sub>2</sub> then we say ''C''<sub>1</sub> and ''C''<sub>2</sub> are '''equivalent'''.
''Lemma'': Any linear code is permutation equivalent to a code which is in standard form.
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