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
-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.
Keywords
self-orthogonal codes, doubly even codes, self-orthogonal
matroids, cocycle, matroids
