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On the Existence of Armstrong Instances with Bounded Domains

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Book cover Foundations of Information and Knowledge Systems (FoIKS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4932))

Abstract

The existence of Armstrong-instances of bounded domains is investigated for specific key systems. This leads to the concept of Armstrong(q,k,n)-codes. These are q-ary codes of length n, minimum distance n − k + 1 and have the property that for any possible k − 1 coordinate positions there are two codewords that agree exactly there. We derive upper and lower bounds on the length of the code as function of q and k. The upper bounds use geometric arguments and bounds on spherical codes, the lower bounds are probabilistic.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O.B. 127, H-1364, Hungary

    Attila Sali

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    László Székely

Authors
  1. Attila Sali
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  2. László Székely
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Sven Hartmann Gabriele Kern-Isberner

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© 2008 Springer-Verlag Berlin Heidelberg

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Sali, A., Székely, L. (2008). On the Existence of Armstrong Instances with Bounded Domains. In: Hartmann, S., Kern-Isberner, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2008. Lecture Notes in Computer Science, vol 4932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77684-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-77684-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77683-3

  • Online ISBN: 978-3-540-77684-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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