  In this work, we find the cardinality of minimal zero short covers of An for
any finite local ring A, removing the restriction of D(A)^2 = 0 from the
previous works in the literature. Using the structure theorem for Artinian
rings, we conclude that we have solved the zero short covering problem for all
finite rings. We demonstrate our results on R_k, an infinite family of finite
commutative rings extensively studied in coding theory, which satisfy D(A)^2
\neq 0 for all k \geq 2.
