Guang-Hui Zhang

A Hyperplane Bound and Ward's Divisibility Conjecture

Let $q=p^f$, where $p$ is prime. We prove that every $q$-ary linear code meeting the Griesmer bound, with positive dimension and minimum distance $d\ge1$, is $p^{\max\{0,\nu_p(d)-f+1\}}$-divisible, as asserted in Ward's conjecture. Arbitrary projective column multiplicities are allowed. The geometric ingredient is a bo...