Planar arcs

The main theorem also verifies the MDS conjecture for a wider range of dimensions in the case that q is an odd square. The MDS conjecture states that if 4⩽k⩽q−2, a k-dimensional linear MDS code has length at most q+1. Here, we verify the conjecture for k⩽q−q/p+2, in the case that q is an odd square.