Advertisement

Combinatorica

, Volume 6, Issue 3, pp 279–285 | Cite as

Orthogonal vectors in then-dimensional cube and codes with missing distances

  • P. Frankl
Article

Abstract

Fork a positive integer letm(4k) denote the maximum number of ±1-vectors of length 4k so that no two are orthogonal. Equivalently,m(4k) is the maximal number of codewords in a code of length 4k over an alphabet of size two, such that no two codewords have Hamming distance 2k. It is proved thatm(4k)=4\(\sum\limits_{0 \leqq i< k} {\left( {\begin{array}{*{20}c} {4k - 1} \\ i \\ \end{array} } \right)} \) ifk is the power of an odd prime.

AMS subject classification (1980)

05 C 35 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ph. Delsarte, On the four principal parameters of a code,Information and Control23 (1973), 407–438.CrossRefMathSciNetzbMATHGoogle Scholar
  2. [2]
    P. Frankl andV. Rödl, Forbidden intersections,Transactions AMS, to appear.Google Scholar
  3. [3]
    P. Frankl andR. M. Wilson, Intersection theorems with geometric consequences,Combinatorica1 (1981), 357–368.zbMATHMathSciNetGoogle Scholar
  4. [4]
    H. Hadwiger, Überdeckungssätze für den Euklidischen Raum,Portugaliae Math.4 (1944), 140–144.zbMATHMathSciNetGoogle Scholar
  5. [5]
    N. Ito, Hadamard graphs,Graphs and Combinatorics1 (1985), 57–64.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    D. G. Larman andC. A. Rogers, The realization of distances within sets in euclidean space,Mathematika19 (1972), 1–24.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    H. Enomoto, P. Frankl, N. Ito, andK. Nomura, Bounds on the size of code: with given distances,Graphs and Combinatorics, to appear.Google Scholar

Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • P. Frankl
    • 1
  1. 1.U.E.R. de MathématiquesUniversité Paris VIIParis Cedex 05France

Personalised recommendations