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.

Proof

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Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes