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New Results on Codes with Covering Radius 1 and Minimum Distance 2

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Abstract

The minimal cardinality of a q-ary code of length n and covering radius at most R is denoted by K q (n, R); if we have the additional requirement that the minimum distance be at least d, it is denoted by K q (n, R, d). Obviously, K q (n, R, d) ≥ K q (n, R). In this paper, we study instances for which K q (n,1,2) > K q (n, 1) and, in particular, determine K4(4,1,2)=28 > 24=K4(4,1).

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Authors and Affiliations

  1. Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015, HUT, Finland

    Patric R. J. Östergård

  2. Helsinki University of Technology, Speckenreye 48, 22119, Hamburg, Germany

    Jörn Quistorff

  3. Department of Mathematics, University of Bayreuth, 95440, Bayreuth, Germany

    Alfred Wassermann

Authors
  1. Patric R. J. Östergård
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  2. Jörn Quistorff
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  3. Alfred Wassermann
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Correspondence to Alfred Wassermann.

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Supported in part by the Academy of Finland under grant 100500.

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Östergård, P.R.J., Quistorff, J. & Wassermann, A. New Results on Codes with Covering Radius 1 and Minimum Distance 2. Des Codes Crypt 35, 241–250 (2005). https://doi.org/10.1007/s10623-005-6404-3

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  • DOI: https://doi.org/10.1007/s10623-005-6404-3

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