2 problems

Let $M$ be an Eulerian binary matroid, viewed as a subset of $\mathbb F_2^n\setminus\{0\}$. Let $c_2(M)$ be the minimum size of an odd-cover of $M$, and let $a(M)$ be the minimum n…

Let $M$ be an Eulerian binary matroid, meaning a subset of $\mathbb F_2^n\setminus\{0\}$ whose elements can be decomposed into circuits. Write $c(M)$ for the minimum number of circ…