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Quasi-perfect codes in the \(\ell _p\) metric

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Abstract

We introduce the notion of degree of imperfection of a code in \(\mathbb {Z}^n\) with the \(\ell _p\) metric, to extend the so-called quasi-perfect codes. Through the establishment of bounds and computational approach, we determine all radii for which there are linear quasi-perfect codes for \(p = 2\) and \(n = 2, 3\). Numerical results concerning the codes with small degree of imperfection are also presented.

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Authors and Affiliations

  1. UNICAMP, University of Campinas, Limeira, SP, 13484-350, Brazil

    João E. Strapasson

  2. UNIFESP, Federal University of São Paulo, São José dos Campos, SP, 12231-280, Brazil

    Grasiele C. Jorge

  3. UNICAMP, University of Campinas, Campinas, SP, 13083-859, Brazil

    Antonio Campello & Sueli I. R. Costa

Authors
  1. João E. Strapasson
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  2. Grasiele C. Jorge
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  3. Antonio Campello
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  4. Sueli I. R. Costa
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Corresponding author

Correspondence to João E. Strapasson.

Additional information

Communicated by Masaaki Harada.

This work was partially supported by FAPESP, Grants 2015/17167-0, 2014/20602-8, 2013/25977-7 and CNPq, Grant 312926/2013-8.

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Strapasson, J.E., Jorge, G.C., Campello, A. et al. Quasi-perfect codes in the \(\ell _p\) metric. Comp. Appl. Math. 37, 852–866 (2018). https://doi.org/10.1007/s40314-016-0372-2

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  • DOI: https://doi.org/10.1007/s40314-016-0372-2

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