An improvement on the Delsarte-type LP-bound with application to MUBs

The linear programming (LP) bound of Delsarte can be applied to several problems in various branches of mathematics. We describe a general Fourier analytic method to get a slight improvement on this bound. We then apply our method to the problem of mutually unbiased bases (MUBs) to prove that the Fourier family $F(a,b)$ in dimension 6 cannot be extended to a full system of MUBs.