Designs, Codes and Cryptography

, Volume 75, Issue 1, pp 97–107 | Cite as

Demi-matroids from codes over finite Frobenius rings

  • Thomas Britz
  • Keisuke Shiromoto
  • Thomas Westerbäck


We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.


Codes over rings Demi-matroid MacWilliams identity 

Mathematics Subject Classification

05B35 94B05 



Thomas Britz and Thomas Westerbäck were partly supported by a UNSW Faculty of Science Silverstar Grant.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Thomas Britz
    • 1
  • Keisuke Shiromoto
    • 2
  • Thomas Westerbäck
    • 3
  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.Department of Mathematics and EngineeringKumamoto UniversityKumamotoJapan
  3. 3.Department of MathematicsKTH Royal Institute of TechnologyStockholmSweden

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