Definition:Coset Decoding Table

Definition
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.


 * 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.

Also see

 * Decoding Received Word using Coset Decoding Table