Definition:Minimum Distance of Linear Code
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Definition
Let $C$ be a linear code whose master code is $\map V {n, p}$.
The minimum distance $d$ of $C$ is defined as:
- $\map d C := \ds \min_{u, v \mathop \in C: u \mathop \ne v} \set {\map d {u, v} }$
where $\map d {u, v}$ denotes the Hamming distance between $u$ and $v$.
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes: Definition $6.8$