On matroids from self-orthogonal codes and their properties

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.