Simplified decoders for projective-geometry codes

A simplified decoding method for projective-geometry codes is presented. The method is based on the mathematical structure of the null space. A detailed analysis of the mathematical structure of the null-space flats of the order-3 (63, 41) projective-geometry code is given and the associated decoder is discussed. Also, the order-5 (255, 218) projective-geometry code and its simplified decoder are studied briefly. It is shown that the resulting decoders require a significantly reduced amount of circuitry as compared with that used in the standard Reed-Muller decoder.