Definition:Error-Correcting Code

Definition

An error-correcting code is a form of encryption that identifies transmission errors, and corrects messages corrupted during transmission.

This is usually done by making the transmitted codeword contain extra characters whose purpose is to detect whether the codeword has been corrupted during transmission.

$k$-Error-Correcting Code

A $k$-error-correcting code is an error-correcting code that can correct up to $k$ transmission errors.

Also see

• Results about error-correcting codes can be found here.

Historical Note

The theory of error-correcting codes was initially developed by Marcel Jules Edouard Golay and Richard Wesley Hamming.

The method has since been used to correct transmission errors on messages received from outer space on space missions to the planets.

As a result, detailed close-up pictures of the planets have been obtained.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): error-correcting code
• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): coding theory
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): error-correcting code
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): coding: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): coding theory
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): error-correcting code