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An extension theorem for arcs and linear codes

  • Coding Theory
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Abstract

We prove the following generalization to the extension theorem of Hill and Lizak: For every nonextendable linear [n, k, d] q code, q = p s, (d,q) = 1, we have

$$\sum\limits_{i\not \equiv 0,d(\bmod q)} {A_i > q^{k - 3} r(q),} $$

where q + r(q) + 1 is the smallest size of a nontrivial blocking set in PG(2, q). This result is applied further to rule out the existence of some linear codes over \(\mathbb{F}_4 \) meeting the Griesmer bound.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, BAS, Sofia, Bulgaria

    I. Landjev

  2. Faculty of Mathematics and Informatics, Sofia University, Bulgaria

    A. Rousseva

Authors
  1. I. Landjev
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  2. A. Rousseva
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Additional information

Original Russian Text © I. Landjev, A. Rousseva, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 4, pp. 65–76.

Supported in part by the NFNI, contract no. M-1405/2005.

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Landjev, I., Rousseva, A. An extension theorem for arcs and linear codes. Probl Inf Transm 42, 319–329 (2006). https://doi.org/10.1134/S0032946006040041

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  • DOI: https://doi.org/10.1134/S0032946006040041

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