Syndrome is Zero iff Vector is Codeword/Mistake
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Source Work
1996: John F. Humphreys: A Course in Group Theory: Chapter $6$: Error-correcting codes
- Proposition $6.20$: Proof
Mistake
- Hence, the element $c$ is a codeword if and only if $c = u G = u \paren {\begin{array} {c|c} I & A \end{array} } = \paren {\begin{array} {c|c} u & v \end{array} }$, where $v = u A$, and $\paren {\begin{array} {c|c} U & v \end{array} }$ denotes the concatenation of $u$ with $v$, ...
Correction
Where it says:
- where ... $\paren {\begin{array} {c|c} U & v \end{array} }$ denotes the concatenation of $u$ with $v$
it should have:
- $\paren {\begin{array} {c|c} u & v \end{array} }$
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes: Proposition $6.20$