Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound

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August 2008, 2(3): 261-272. doi: 10.3934/amc.2008.2.261

Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound

J. De Beule ^1, , K. Metsch ^2, and L. Storme ^1,

1.	Dept. of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium, Belgium
2.	Mathematisches Institut, Universität Gieβen, Arndtstraβe 2, D-35392 Gieβen, Germany

Received January 2008 Published July 2008

Abstract
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We present characterization results on weighted minihypers. We prove the weighted version of the original results of Hamada, Helleseth, and Maekawa. Following from the equivalence between minihypers and linear codes meeting the Griesmer bound, these characterization results are equivalent to characterization results on linear codes meeting the Griesmer bound.

Keywords: Griesmer bound, Minihypers, blocking sets..

Mathematics Subject Classification: 05B25, 51E20, 51E21, 94B0.

Citation: J. De Beule, K. Metsch, L. Storme. Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound. Advances in Mathematics of Communications, 2008, 2 (3) : 261-272. doi: 10.3934/amc.2008.2.261

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