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Extremal and Optimal Codes

  • Gabriele Nebe
  • Eric M. Rains
  • Neil J.A. Sloane
Chapter
  • 992 Downloads
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 17)

Abstract

A basic problem in coding theory is to find codes with large minimal distance (Hamming, Lee, or Euclidean distance, as appropriate). In order to decide if a particular code is good, it is necessary to know how good comparable codes could be; that is, for a given length and dimension, what is the optimal minimal distance? For general codes, this question is discussed in many references—see for example [361, Chap. 17], and Chapters 4 (by Brouwer [84]), 5 (by Levenshtein [352]), and 6 (by Litsyn [348]) of The Handbook of Coding Theory [426]. In the present book, of course, we are interested in self-dual codes. As one might imagine, the constraint of self-duality usually leads to stronger bounds.

Keywords

Optimal Code Weight Enumerator Extremal Type Unimodular Lattice Negacyclic Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • Gabriele Nebe
    • 1
  • Eric M. Rains
    • 2
  • Neil J.A. Sloane
    • 3
  1. 1.Lehrstuhl D für Mathematik Rheinisch-Westfälische Technische Hochschule AachenAachenGermany
  2. 2.Department of MathematicsUniversity of California at DavisDavisUSA
  3. 3.Internet and Network Systems Research AT&T Shannon LabsFlorham ParkUSA

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