This work investigates the hardness of computing sparse solutions to systems of linear equations over $\mathbb{F}_2$. Consider the $k$-EvenSet problem: given a homogeneous system of linear equations over $\mathbb{F}_2$ on $n$ variables, decide if there exists a nonzero solution of Hamming weight at most $k$ (i.e. a $k$-sparse solution). While ... more >>>