nLab coding theory

Idea

From Judson 2012:

Coding theory is an application of algebra that has become increasingly important over the last several decades. When we transmit data, we are concerned about sending a message over a channel that could be affected by “noise.” We wish to be able to encode and decode the information in a manner that will allow the detection, and possibly the correction, of errors caused by noise. This situation arises in many areas of communications, including radio, telephone, television, computer communications, and even compact disc player technology. Probability, combinatorics, group theory, linear algebra, and polynomial rings over finite fields all play important roles in coding theory.

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Related entries

• error correcting codes

  • linear code

    • Hamming code

    • binary linear code

      • binary Golay code, Mathieu group, Leech lattice

• quantum error correcting code

  • stabilizer code

  • HaPPY code

  • Majorana dimer code

• combinatorial design

• adinkra

References

• Thomas W. Judson: Algebraic Coding Theory, Chapter 8: in: Abstract Algebra: Theory and Applications, lecture notes (2012) [pdf]

• T. Etzion, L. Storme, Galois geometries and coding theory, Designs, Codes and Cryptography 78:1 (2016) 311-350 doi

• Patrick J. Morandi, Error Correcting Codes and Algebraic Curves, lecture notes New Mexico State University 2001. (pdf)

• Jay A. Wood: Spinor groups and algebraic coding theory, J.Combinatorial Th. Series A 51 (1989) 277–313 [doi:10.1016/0097-3165(89)90053-8]