Decoding Received Word using Coset Decoding Table

Theorem
Let $C$ be a linear code.

Let $v$ be a received word, which may have transmission errors.

To find out the transmitted codeword $u$ corresponding to $v$:


 * $(1): \quad$ Find $v$ in the coset decoding table for $C$.


 * $(2): \quad$ The corresponding transmitted codeword $u$ will be found at the top of the column where $v$ can be found.