Advertisement

Constant Weight Codes with Package CodingTheory.m in Mathematica

  • Igor Gashkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)

Abstract

The author offers the further development of package CodingTheory.m [1] in the direction of research of properties and parameters of Constant weight codes (lower and upper bounds) based on works [2], [3] and also using the Table of Constant Weight Binary Codes (online version, Neil J. A. Sloane: Home Page http://www.research.att.com/ njas/codes/Andw/) and the table of upper bounds on A(n, d, w) (which in many cases also gives lower bounds) maintained by Erik Agrell, Alexander Vardy and Kenneth Zeger, and which is an electronic supplement to their paper Upper bounds for constant-weight codes, http://www.s2.chalmers.se/~agrell/bounds/cw.html. The offered package allows to carry out the comparative analysis of parameters of new codes with classical upper bounds such as Johnson bound, Linear programming (Ph Delsarte) bound ..., and also with already available classes of codes. As an example we consider a some construction of codes as union of two codes with parameters (n, 2a, a + b) and (m, 2b, a + b), that in some cases gives codes the best than codes obtained with use Juxtaposing.

References

  1. 1.
    Gachkov, I.: Error Correcting codes with Mathematica. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 737–746. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Brouwer, E., Shearer, J.B., Sloane, N.J.A.: A new table of Constant weight codes. IEEE Transactions of information theory 36(6) (1990)Google Scholar
  3. 3.
    Agrell, E., Vardy, A., Zeger, K.: Upper bounds for constant-weight codes. IEEE Transactions on Information Theory 46(7), 2373–2395 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Igor Gashkov
    • 1
  1. 1.Department of Engineering Sciences, Physics and MathematicsKarlstad UniversityKarlstadSweden

Personalised recommendations