\begin{definition}[Definition:Coset Decoding Table]
A '''coset decoding table''' is a technique for decoding a linear $\tuple {n, k}$ code.
Let $C$ be a linear $\tuple {n, k}$ code whose master code is $\map V {n, p}$.
Let $T$ be an array constructed as follows:
:The first row consists of the codewords of $C$, starting with the zero codeword first.
{{explain|It has not yet been rigorously proved that $C$ does actually contain the zero codeword.}}
:Each subsequent row is a left coset of $C$.
:The entries of the first column of $T$ are the coset representatives, now called '''coset leaders'''.
:The $r$th coset leader is allocated by choosing any element of $\map V {n, p}$ of minimum weight which is not already included in the first $r - 1$ rows.
Then $T$ is a '''coset decoding table'''.
Note that it may not always be easy to find the $r$th coset leader.
\end{definition}