IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-93806-4_4.html
   My bibliography  Save this book chapter

An Introduction to Linear and Cyclic Codes

In: Gröbner Bases, Coding, and Cryptography

Author

Listed:
  • Daniel Augot

    (INRIA Paris-Rocquencourt)

  • Emanuele Betti

    (University of Florence, Department of Mathematics)

  • Emmanuela Orsini

    (University of Milan, Department of Mathematics)

Abstract

Our purpose is to recall some basic aspects about linear and cyclic codes. We first briefly describe the role of error-correcting codes in communication. To do this we introduce, with examples, the concept of linear codes and their parameters, in particular the Hamming distance. A fundamental subclass of linear codes is given by cyclic codes, that enjoy a very interesting algebraic structure. In fact, cyclic codes can be viewed as ideals in a residue classes ring of univariate polynomials. BCH codes are the most studied family of cyclic codes, for which some efficient decoding algorithms are known, as the method of Sugiyama.

Suggested Citation

  • Daniel Augot & Emanuele Betti & Emmanuela Orsini, 2009. "An Introduction to Linear and Cyclic Codes," Springer Books, in: Massimiliano Sala & Shojiro Sakata & Teo Mora & Carlo Traverso & Ludovic Perret (ed.), Gröbner Bases, Coding, and Cryptography, pages 47-68, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-93806-4_4
    DOI: 10.1007/978-3-540-93806-4_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-540-93806-4_4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.