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Parameters for which the Griesmer bound is not sharp

Authors :
Andreas Klein
Klaus Metsch
Source :
Discrete Mathematics. (22):2695-2703
Publisher :
Elsevier B.V.

Abstract

We prove for a large class of parameters t and r that a multiset of at most [email protected]"d"-"[email protected]"d"-"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].

Details

Language :
English
ISSN :
0012365X
Issue :
22
Database :
OpenAIRE
Journal :
Discrete Mathematics
Accession number :
edsair.doi.dedup.....b58e3ca95547a19c3251d3bc01d96b9a
Full Text :
https://doi.org/10.1016/j.disc.2007.01.015