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The non-existence of Griesmer codes with parameters close to codes of Belov type

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Abstract

Hill and Kolev give a large class of q-ary linear codes meeting the Griesmer bound, which are called codes of Belov type (Hill and Kolev, Chapman Hall/CRC Research Notes in Mathematics 403, pp. 127–152, 1999). In this article, we prove that there are no linear codes meeting the Griesmer bound for values of d close to those for codes of Belov type. So we conclude that the lower bounds of d of codes of Belov type are sharp. We give a large class of length optimal codes with n q (k, d) = g q (k, d) + 1.

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Authors and Affiliations

  1. Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Korea

    E. J. Cheon

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  1. E. J. Cheon
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Correspondence to E. J. Cheon.

Additional information

Communicated by R. Hill.

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-532-C00001).

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Cheon, E.J. The non-existence of Griesmer codes with parameters close to codes of Belov type. Des. Codes Cryptogr. 61, 131–139 (2011). https://doi.org/10.1007/s10623-010-9443-3

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  • DOI: https://doi.org/10.1007/s10623-010-9443-3

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