A shared encoder/decoder circuit for use with a Reed-Solomon coding scheme of an optical disk storage system. The optical disk system includes a drive adapted to permanently store data on a removable platter. Prior to recording a data byte on the platter, the data is encoded with a Reed-Solomon code. When the data is read from the disk, it is decoded and error correction syndromes are generated. The same circuitry is shared for performing the encoding and decoding functions. This circuitry includes independent sets of a RAM, coupled to one input of an exclusive OR (modulo two sum) adding circuit. The output of the adding circuit is fed back to an input to the RAM. Two multiplier circuits are coupled to the output of the RAM. A product of one is tied to one input of the modulo two addition circuit. The product of the other is combined with similar products from other sets, and the resulting combination signal is selectively connected to the other input of the modulo two addition circuit, along with data to be recorded on the platter, or data read from the platter.