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Encyclopedia of Cryptography and Security pp 291–294Cite as

Cyclic Codes

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Synonyms

Error-correcting cyclic codes

Related Concepts

Finite Field; Information Theory

Definition

A cyclic code of length n is an error-correcting block code, with block length n, which contains all n cyclic shifts of any codeword.

Background

Coding theory

Theory

For a general presentation of cyclic codes, the main reference is the Handbook of Coding Theory, especially the first chapter [4] (but also Chapters 11, 13, 14, and 19).

Cyclic codes were introduced as a particular practical class of error-correcting codes (ECC). Codes are devoted to the following fundamental problem: how to determine what message has been sent when only an approximation is received, due to a noisy communication channel. Cyclic codes belong to the class of block codes: since all messages have here the same length k.Each of them is encoded into a codeword of length n=k+r.A t-error-correcting code is a well-chosen subset C of \({\mathcal{A}}^{n}.\) Its elements are called codewordsand have the property that...

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Recommended Reading

  1. Canteaut A, Charpin P, Dobbertin H (1999) A new characterization of almost bent functions. In Fast software encryption (FSE6), LNCS 1636. Springer, New York, pp 186–200

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  2. Carlet C, Charpin P, Zinoviev V (1998) Codes, bent functions and permutations suitable for DES-like cryptosystems. Design Code Cryptogr 15(2):125–156

    Article  MATH  MathSciNet  Google Scholar 

  3. McEliece RJ, Sarwarte DV (1981) On sharing secrets and Reed-Solomon codes. Commun ACM 24:583–584

    Article  Google Scholar 

  4. Pless VS, Huffman WC, Brualdi RA (1998) An introduction to algebraic codes. Handbook of coding theory, part 1: algebraic coding, chapter 1. Elsevier, Amsterdam

    Google Scholar 

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Author information

Authors and Affiliations

  1. INRIA, Domaine de Voluceau, B.P. 105, F-78153, Rocquencourt, Le Chesnay Cedex, France

    Pascale Charpin (Dr.)

Authors
  1. Pascale Charpin
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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Charpin, P. (2011). Cyclic Codes. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_343

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