Demi-matroids from codes over finite Frobenius rings

Thomas Britz*, Keisuke Shiromoto, Thomas Westerbäck

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)97-107
Number of pages11
JournalDESIGNS CODES AND CRYPTOGRAPHY
Volume75
Issue number1
DOIs
Publication statusPublished - 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Codes over rings
  • Demi-matroid
  • MacWilliams identity

Fingerprint Dive into the research topics of 'Demi-matroids from codes over finite Frobenius rings'. Together they form a unique fingerprint.

Cite this