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International Conference on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 1988: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 396–406Cite as

A covering problem in the odd graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 357))

Abstract

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.

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Author information

Authors and Affiliations

  1. School of Computer and Information Science, Syracuse University, 13244-1240, Syracuse, NY

    Patrick Solé

  2. Dept. of Electrical and Computer Engr., Syracuse University, 13244-1240, Syracuse, NY

    Arif Ghafoor

Authors
  1. Patrick Solé
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  2. Arif Ghafoor
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Editor information

Teo Mora

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© 1989 Springer-Verlag Berlin Heidelberg

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Solé, P., Ghafoor, A. (1989). A covering problem in the odd graphs. In: Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1988. Lecture Notes in Computer Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51083-4_75

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  • DOI: https://doi.org/10.1007/3-540-51083-4_75

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51083-3

  • Online ISBN: 978-3-540-46152-4

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