Designs, Codes and Cryptography

, Volume 81, Issue 1, pp 169–178 | Cite as

A generalization of Kung’s theorem

  • Trygve Johnsen
  • Keisuke Shiromoto
  • Hugues Verdure


We give a generalization of Kung’s theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all \(i=k+1,\ldots ,n\), we give an upper bound on the smallest integer m such that there exist m codewords whose union of supports has cardinality at least i.


Linear code Kung’s bound Generalized Singleton bound 

Mathematics Subject Classification

94B05 05E40 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Trygve Johnsen
    • 1
  • Keisuke Shiromoto
    • 2
  • Hugues Verdure
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of TromsøTromsøNorway
  2. 2.Department of Mathematics and EngineeringKumamoto UniversityKumamotoJapan

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