Positive Independence and Enumeration of Codes with a Given Distance Pattern

  • M. Deza
  • D. K. Ray-Chaudhuri
  • N. M. Singhi
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)


A concept of P-independent sets is defined for Z-modules or convex sets. P- independence gives a convex analogue of usual independence. It is used for codes. A quasipolynomial type theorem is proved for the number of inequivalent codes with a given distance pattern and length. The relationships with the classical coding problem and the design problem are discussed.


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  1. [A]
    Assouad,P., Sous espaces de l’ et inequalités hypermetriques, C.R. Acad. Sci., Paris 294, Series A (1982), pp. 439–442.MathSciNetzbMATHGoogle Scholar
  2. [AD]
    Assouad, P. and Deza, M., Metric subspaces of L1, Publ. Math. d’Orsay, Universite, Paris-Sud (1982).Google Scholar
  3. [D1]
    Deza, M. (Tylkin), Realizability of matrices of distance in unitary cubes (in Russian), Prol. Kibem, 7 (1962), pp. 31–42.Google Scholar
  4. [D2]
    Deza, M., Isometries of the hypergraphs, Proc. Int. Conference on Theory of Graphs, Calcutta, (ed. A.E. Rao) (1977); McMillan, India (1979), pp. 174–189.Google Scholar
  5. [D3]
    Deza, M., Small Pentagonal spaces, Rendiconti del Seminario Matematico di’ brescia, Volume settino (1984), pp. 269–282.Google Scholar
  6. [DR]
    Deza, M. and Rosenberg, I.G., Intersections and distance patterns, Util. Math., 25 (1984), pp. 191–212.MathSciNetzbMATHGoogle Scholar
  7. [DS]
    Deza, M. and Singhi N.M., Rigid Pentagons in Hypercubes, Graphs and Combinaterics, 4 (1988), pp. 31–42.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [R]
    Ryser, H., Combinaterial Mathematics, the Cams Mathematical Monographs, no. 14, The Mathematical Association of America.Google Scholar
  9. [RS1]
    Ray-Chaudhuri, D.K. and Singhi, N.M., On existence and number of orthogonal arrays, J. of Combinatorial Theory A, 47 (1988), pp. 28–36.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [RS2]
    Ray-Chaudhuri, D.K. and Singhi, N.M., q-analogues of t-designs and their existence, Linear Algebra And Its Applications, 114/115 (1989), pp. 57–68.Google Scholar
  11. [S]
    Stanley, R., Combinatorics and Commutative Algebra, Birkhäuser, Boston (1983).zbMATHGoogle Scholar
  12. [SS]
    Singhi, N.M., and Shrikhande, S.S., A reciprocity relation for t-designs, Europ. J. Combinatorics, 8 (1987), pp. 59–68.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • M. Deza
    • 1
  • D. K. Ray-Chaudhuri
    • 2
  • N. M. Singhi
    • 3
  1. 1.C.N.E.S. UA 212Université Paris 7France
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA
  3. 3.School of MathematicsTata Institute of Fundamental ResearchColaba, BombayIndia

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