Decoding methods: Difference between revisions

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Holting (talk | contribs)
m The set of possible errors in a binary code is not strictly smaller than \abs{C}, consider e.g. the repetition code. The lookup table only becomes smaller compared to the full standard array of the code.
Line 115:
:<math>
\begin{matrix}
\sum_{i=0}^t \binom{n}{i} < |C| \\
\end{matrix}
</math>
 
only (for a binary code). The table is against pre-computed values of <math>He</math> for all possible error patterns <math>e \in \mathbb{F}_2^n</math>.
 
Knowing what <math>e</math> is, it is then trivial to decode <math>x</math> as: