A covering problem in the odd graphs

  • Patrick Solé
  • Arif Ghafoor
Full Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 357)


The following problem originated in the design of interconnection networks: what is the graphical covering radius of an Hadamard code of length 2k−1 and size 2k−1 in the Odd graph O k ? Of particular interest is the case of k=2m−1, where we can choose this Hadamard code to be a subcode of the punctured first order Reed-Muller code RM(1,m). We define the w-covering radius of a binary code as the largest Hamming distance from a binary word of Hamming weight w to the code. The above problem amounts to finding the k-covering radius of a (2k, 4k) Hadamard code. We find upper and lower bounds on this integer, and determine it for small values of k.

Key words

Interconnection Networks Coding Theory Covering Radius Odd Graphs Hadamard Matrices First order Reed Muller Code Coset weight distribution 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Patrick Solé
    • 1
  • Arif Ghafoor
    • 2
  1. 1.School of Computer and Information ScienceSyracuse UniversitySyracuse
  2. 2.Dept. of Electrical and Computer Engr.Syracuse UniversitySyracuse

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