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''Lemma'' ([[Singleton bound]]): Every linear [n,k,d] code C satisfies <math>k+d \leq n+1</math>.
A code C whose parameters satisfy k+d=n+1 is called '''maximum distance separable''' or '''MDS'''. Such codes, when they exist, are in
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'''.
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