On two-weight (linear and nonlinear) codes

We consider q-ary (linear and nonlinear) block codes with exactly two distances: d and d+δ. We obtain, as a necessary condition, a quadratic equation which relates the length n of the code to the remaining parameters. We also obtain upper bounds for the maximum size of such codes by utilizing a useful relation with two-distance spherical codes. Three tables of lower and upper bounds for alphabet sizes q =2, 3 and 4, respectively, are presented as examples.