  We recover the first linear programming bound of McEliece, Rodemich, Rumsey,
and Welch for binary error-correcting codes and designs via a covering
argument. It is possible to show, interpreting the following notions
appropriately, that if a code has a large distance, then its dual has a small
covering radius and, therefore, is large. This implies the original code to be
small.
  We also point out (in conjunction with further work) that this bound is a
natural isoperimetric constant of the Hamming cube, related to its Faber-Krahn
minima.
  While our approach belongs to the general framework of Delsarte's linear
programming method, its main technical ingredient is Fourier duality for the
Hamming cube. In particular, we do not deal directly with Delsarte's linear
program or orthogonal polynomial theory.
