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Antichain Codes

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Abstract

We show that almost all codes satisfy an antichain condition. This states that the minimum length of a two dimensional subcode of a code C increases if the subcode is constrained to contain a minimum weight codeword. In particular, almost no code satisfies the chain condition. In passing, we study the typical behaviour of codes with respect to generalized distances and show that almost all lie on a generalized Varshamov-Gilbert bound.

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References

  1. E. F. Assmus Jr., and J. D. Key, Designs and Their Codes, Cambridge University Press (1992).

  2. T. Beth, D. Jungnickel, and H. Lenz, Design Theory, BI Wissenschaftsverlag (1985).

  3. G. D. Cohen and G. Zémor, Intersecting codes and independent families, IEEE Transactions on Information Theory, Vol. 40 (1994) pp. 1872-1881.

    Google Scholar 

  4. S. Encheva and T. Kløve, Codes satisfying the chain condition, IEEE Transactions on Information Theory, Vol. 40 (1994) pp. 175-180.

    Google Scholar 

  5. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam (1977).

    Google Scholar 

  6. J. L. Massey, D. J. Costello, Jr., and J. Justesen, Polynomial weights and code constructions, IEEE Transactions on Information Theory, Vol. 19 (1973) pp. 101-110.

    Google Scholar 

  7. V. N. Koshelev, On some properties of random group codes, Problems of Information Transmission, Vol. 1,No. 4 (1965) pp. 35-38.

    Google Scholar 

  8. L. H. Ozarow and A. D. Wyner, Wire-tap channel II, AT&T Bell Labs. Techn. J., Vol. 63 (1984) pp. 2137-2157.

    Google Scholar 

  9. J. N. Pierce, Limit distribution of the minimum distance of random linear codes, IEEE Transactions on Information Theory, Vol. 13 (1967) pp. 595-599.

    Google Scholar 

  10. V. K. Wei, Generalized Hamming weights for linear codes, IEEE Transactions on Information Theory, Vol. 37 (1991) pp. 1412-1418.

    Google Scholar 

  11. V. K. Wei and K. Yang, On the generalized Hamming weights of product codes, IEEE Transactions on Information Theory, Vol. 39 (1993) pp. 1709-1713.

    Google Scholar 

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Authors and Affiliations

  1. ENST, 46 rue Barrault, 75634, Paris Cedex 13, France

    Gérard D. Cohen & Gilles Zémor

  2. Stord/Haugesund College, Skaareg. 103, 5500, Haugesund, Norway

    Sylvia B. Encheva

Authors
  1. Gérard D. Cohen
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  2. Sylvia B. Encheva
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  3. Gilles Zémor
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Cohen, G.D., Encheva, S.B. & Zémor, G. Antichain Codes. Designs, Codes and Cryptography 18, 71–80 (1999). https://doi.org/10.1023/A:1008329017752

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  • DOI: https://doi.org/10.1023/A:1008329017752

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