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On the Length of Codes with a Given Covering Radius

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Coding Theory and Design Theory

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 20))

Abstract

We further develop techniques for showing the non-existence of short codes with a given covering radius. In particular we show that there does not exist a code of codimension 11 and covering radius 2 which has length 64. We conclude with a table which gives the best available information for the length of a code with codimension m and covering radius r for 2 ≤ m ≤ 24 and 2 ≤ r ≤ 24.

*Research partially supported by National Science Foundation Grant No. DMS-8421521

Research partially supported by National Security Agency Grant No. MDA 904-85-H-0016

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References

  1. D. Ashlock. private communication.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Richard A. Brualdi

  2. Department of Mathematics, University of Illinois at Chicago, Chicago, IL, 60680, USA

    Vera S. Pless

Authors
  1. Richard A. Brualdi
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  2. Vera S. Pless
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© 1990 Springer-Verlag New York, Inc.

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Brualdi, R.A., Pless, V.S. (1990). On the Length of Codes with a Given Covering Radius. In: Coding Theory and Design Theory. The IMA Volumes in Mathematics and Its Applications, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8994-1_2

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  • DOI: https://doi.org/10.1007/978-1-4613-8994-1_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8996-5

  • Online ISBN: 978-1-4613-8994-1

  • eBook Packages: Springer Book Archive

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