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Covering radius of RM(1,9) in RM(3,9)

  • Philippe Langevin
Section 1 Algebraic Codes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 514)

Abstract

We give new properties about Fourier coefficients and we prove that the distance of the first order Reed-Muller code of length 512 to any cubic is at most 240.

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Bibliography

  1. [1]
    O. S. Rothaus, On "bent" functions, J.C.T. 20 (1976), 300–305.CrossRefGoogle Scholar
  2. [2]
    E. Berlekamp and L.R. Welch, Weigth distributions of the cosets of the (32,6) Reed-Muller code, IEEE T. I. T., vol. IT-18 (1972), 203–207.Google Scholar
  3. [3]
    T. Helleseth, T. Klove, and J. Mykkelveit, On the covering radius of binary codes, IEEE T.I.T. vol. IT-24 (1978), 627–628.Google Scholar
  4. [4]
    J. Mykkelveit, The covering radius of the (128,8) Reed-Muller code is 56. IEEE T.I.T. vol-26 (1980) 359–362.Google Scholar
  5. [5]
    N.J. Patterson and D.H. Wiedemann, The covering radius of the (215,16) Reed-Muller code is at least 16276, IEEE T.I.T. vol IT-29 (1983) 354–356.Google Scholar
  6. [6]
    J. Constantin, B. Courteau and J. Wolfmann, Numerical experiments related to the covering radius of some first order Reed-Muller codes.Google Scholar
  7. [7]
    F.J.S. Mac Williams and N.J.A. Sloane, The theory of error correcting codes, North Holland.Google Scholar
  8. [8]
    G.D. Cohen, M.G. Karpovsky, H.F. Mattson, Jr. and J.R. Schatz Covering radius — Survey and Recent Results IEEE T.I.T. vol-31 (1985), (328–344).Google Scholar
  9. [9]
    R.A. Brualdi and V.S. Pless, Orphans of the first order Reed-Muller codes. IEEE T.I.T., vol I.T-18 (1972), (203–207).Google Scholar
  10. [10]
    R.A. Brualdi,N. Cai, and V.S. Pless, Orphan Structure of the first order Reed-Muller codes.Google Scholar
  11. [11]
    J.R Joly, Equations et variétés algébriques sur un corps fini in L'enseignement des mathématiques, t.XIX, fasc 1–2.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Philippe Langevin
    • 1
  1. 1.G.E.C.T.Université de ToulonLa GardeFrance

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