The circular horn gain is that of a uniform distribution minus a gain due to quadratic phase error and the amplitude tapers across the aperture.  We can use these scales to design horns with the same gain and different slant radiuses for either smooth-wall or corrugated-wall horns. The downloaded executables will also perform calculations in a DOS window.
Cir_Horn_eff.gif
          CIRHDN (Linux version) – Circular TE11 mode design to gain
          CIRBWD (Linux version) – Circular TE11 mode design to beamwidth
          HORNCI (Linux version) – Circular TE11 mode parameters given dimensions
          CORHDN (Linux version) – Balanced hybrid mode corrugated horn designed to gain
          CORBWD (Linux version) – Balanced hybrid mode corrugated horn designed to beamwidth
          HORNCO (Linux version) – Balanced hybrid mode corrugated horn parameters from dimensions