Graphs and Combinatorics

, Volume 3, Issue 1, pp 25–38 | Cite as

Codes with given distances

  • H. Enomoto
  • P. Frankl
  • N. Ito
  • K. Nomura


One of the main results says that ifC is a binary linear code of length 4t and of dimension greater than 2t, thenC contains a word of weight 2t and this bound is best possible. Several results of similar flavor are established both for linear and non-linear codes. For the proof a lemma introducing the binormal forms of binary matrices is needed. The results are applied to determine the coset chromatic number of Hadamard graphs, to solve a problem of Galvin and to give a short proof of a theorem of Gleason on self-dual doubly-even codes.


Linear Code Chromatic Number Short Proof Binary Matrice Binary Linear 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-Verlag 1987

Authors and Affiliations

  • H. Enomoto
    • 1
  • P. Frankl
    • 2
  • N. Ito
    • 3
  • K. Nomura
    • 4
  1. 1.Department of Information ScienceUniversity of TokyoTokyoJapan
  2. 2.CNRS, Quai Anatole FranceParisFrance
  3. 3.Department of Applied MathematicsKonan UniversityKobeJapan
  4. 4.Department of MathematicsTokyo Ikashika UniversityKonodai, IchikawaJapan

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