On matroids from self-orthogonal codes and their properties

Weston Loucks, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review


Matroids and codes are closely related. In the binary case, they are essentially identical. In algebraic coding theory, self-orthogonal codes, and a special type of these called self-dual codes, play an important role because of their connections with t-designs. In this work, we further explore these connections by introducing the notions of cycle-nested and doubly even matroids. In the binary case, we characterize the cocycle-nested matroids and describe some properties of doubly even matroids by relating them to doubly even codes. We also relate the concept of self-orthogonal realizations with Eulerian matroids.

Original languageEnglish (US)
Pages (from-to)409-420
Number of pages12
Issue number3
StatePublished - 2023
Externally publishedYes


  • cocycle
  • doubly even codes
  • matroids
  • self-orthogonal codes
  • self-orthogonal matroids

ASJC Scopus subject areas

  • General Mathematics


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