Error-correcting codes are used to protect data from random errors in satellite and wireless communication systems, audio and video recording devices, and data storage devices. A large class of codes with a wide range of applications are based on finite geometry. The most notable example of such codes are the Reed-Muller codes that are being used in deep space and mobile communications.

The subject of this talk is a class of codes based on combinatorial designs. These combinatorial codes possess remarkable error-correction properties, admit efficient decoding, and present a viable alternative to a subclass of Reed-Muller codes.