Designs, Codes and Cryptography

, Volume 65, Issue 1–2, pp 5–14 | Cite as

On sets of vectors of a finite vector space in which every subset of basis size is a basis II

  • Simeon Ball
  • Jan De Beule


This article contains a proof of the MDS conjecture for k ≤ 2p − 2. That is, that if S is a set of vectors of \({{\mathbb F}_q^k}\) in which every subset of S of size k is a basis, where q = p h , p is prime and q is not and k ≤ 2p − 2, then |S| ≤ q + 1. It also contains a short proof of the same fact for k ≤ p, for all q.


MDS conjecture Linear codes Singleton bound 

Mathematics Subject Classification

51E21 15A03 94B05 05B35 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departament de Matemàtica Aplicada IVUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Department of MathematicsGhent UniversityGhentBelgium

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