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Algebraic Coding Theory

  1. Tor Helleseth,
  2. Torleiv Kløve

Published Online: 14 DEC 2007

DOI: 10.1002/9780470050118.ecse011

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Helleseth, T. and Kløve, T. 2007. Algebraic Coding Theory. Wiley Encyclopedia of Computer Science and Engineering. .

Author Information

  1. University of Bergen, Bergen, Norway

Publication History

  1. Published Online: 14 DEC 2007

Abstract

In computers and digital communication systems, information almost always is represented in a binary form as a sequence of bits each having the values 0 or 1. This sequence of bits is transmitted over a channel from a sender to a receiver. In some applications the channel is a storage medium like a DVD, where the information is written to the medium at a certain time and retrieved at a later time. Because of the physical limitations of the channel, some transmitted bits may be corrupted (the channel is noisy) and thus make it difficult for the receiver to reconstruct the information correctly.

In algebraic coding theory, we are concerned mainly with developing methods to detect and correct errors that typically occur during transmission of information over a noisy channel. The basic technique to detect and correct errors is by introducing redundancy in the data that is to be transmitted. This article we describe the basic ideas, give some codes that are most important for applications, and explain their decoding algorithms. In particular, we describe the Reed–Solomon codes and give both the classic Berlekamp–Massery decoging algorithm and the recent Guruswami–Sudan decoding algorighm.

Keywords:

  • coding theory;
  • decoding;
  • Reed–Solomon codes