The non-existence of Griesmer codes with parameters close to codes of Belov type
The non-existence of Griesmer codes with parameters close to codes of Belov type
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DOI：
10.1007/s10623-010-9443-3
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发表时间：
2011-11
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影响因子：
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通讯作者：
E. J. Cheon
中科院分区：
文献类型：
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作者：
E. J. Cheon
Hill和Kolev给出了满足Griesmer界的一大类q元线性码，其被称为Belov型码（Hill和Kolev，Chapman Hall/CRC Research Notes in Mathematics 403，pp. 127-152，1999）。在这篇文章中，我们证明了没有线性码满足Griesmer界的值d接近那些Belov型码。从而得出结论：Belov型dof码的下界是尖锐的.本文给出了一大类长度最优码，其中nq（k，d）=gq（k，d）+ 1.
Hill and Kolev give a large class ofq-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 ofdclose to those for codes of Belov type. So we conclude that the lower bounds ofdof codes of Belov type are sharp. We give a large class of length optimal codes withnq(k,d) =gq(k,d) + 1.