On the nonexistence of q-ary linear codes of dimension five
There do not exist [n, 5, d] codes over the Galois field GF(q) attaining the Griesmer bound for d = q(4) - 2q(2) - q + 1. 2q(4) - 2q(3) - q(2) - q + 1 for q greater than or equal to 3 and for d = 3q(4) - 4q(3) = q + 1 for q greater than or equal to 5.
linear codes the griesmer bound projective spaces