Parameters for which the Griesmer bound is not sharp |
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Authors: | Andreas Klein |
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Affiliation: | a Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium b Mathematisches Institut, Arndtstrasse 2, D-35392 Giessen, Germany |
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Abstract: | We prove for a large class of parameters t and r that a multiset of at most tθd-k+rθd-k-2 points in PG(d,q) that blocks every k-dimensional subspace at least t times must contain a sum of t subspaces of codimension k.We use our results to identify a class of parameters for linear codes for which the Griesmer bound is not sharp. Our theorem generalizes the non-existence results from Maruta [On the achievement of the Griesmer bound, Des. Codes Cryptogr. 12 (1997) 83-87] and Klein [On codes meeting the Griesmer bound, Discrete Math. 274 (2004) 289-297]. |
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Keywords: | Codes Griesmer bound Blocking sets |
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