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

Pages: 261 - 272, Volume 2, Issue 3, August 2008      doi:10.3934/amc.2008.2.261

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J. De Beule - Dept. of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium (email)
K. Metsch - Mathematisches Institut, Universität Gieβen, Arndtstraβe 2, D-35392 Gieβen, Germany (email)
L. Storme - Dept. of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium (email)

Abstract: 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:  Minihypers, Griesmer bound, blocking sets.
Mathematics Subject Classification:  05B25, 51E20, 51E21, 94B05.

Received: January 2008;      Available Online: July 2008.