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New Linear Codes with Covering Radius 2 and Odd Basis

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Abstract

On the way of generalizing recent results by Cock and the second author, it is shown that when the basis q is odd, BCH codes can be lengthened to obtain new codes with covering radius R=2. These constructions (together with a lengthening construction by the first author) give new infinite families of linear covering codes with codimension r=2k+1 (the case q=3, r=4k+1 was considered earlier). New code families with r=4k are also obtained. An updated table of upper bounds on the length function for linear codes with ≤ 24, R=2, and q=3,5 is given.

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Authors and Affiliations

  1. Institute for Problems of Information Transmission, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, GSP-4, Moscow, 101447, Russia

    Alexander A. Davydov

  2. Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015, HUT, Finland

    Patric R. J. Osterga

Authors
  1. Alexander A. Davydov
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  2. Patric R. J. Osterga
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Davydov, A.A., Osterga, P.R.J. New Linear Codes with Covering Radius 2 and Odd Basis. Designs, Codes and Cryptography 16, 29–39 (1999). https://doi.org/10.1023/A:1008370224461

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  • DOI: https://doi.org/10.1023/A:1008370224461

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