Mappings between codewords of two distinct (n,k) reed-solomon codes over

Abstract

A process for realizing mappings between codewords of two distinct (N,K) Reed-Solomon codes over GF(2.sup.J) having selected two independent parameters: J, specifying the number of bits per symbol; and E, the symbol error correction capability of the code, wherein said independent parameters J and E yield the following: N=2.sup.J -1, total number of symbols per codeword; 2E, the number of symbols assigned a role of check symbols; and K=N-2E, the number of code symbols representing information, all within a codeword of an (N,K) RS code over GF(2.sup.J), and having selected said parameters for encoding, the implementation of a decoder are governed by: 2.sup.J field elements defined by a degree J primitive polynomial over GF(2) denoted by F(x); a code generator polynomial of degree 2E containing 2E consecutive roots of a primitive element defined by F(x); and, in a Berlekamp RS code, the basis in which the RS information and check symbols are represented. The process includes separate transformation steps for symbol-by-symbol conversion for a first RS code to ultimately a second conventional RS code capable of being corrected by a conventional RS decoder, followed by a reverse sequence of the inverse of the first set of steps to arrive at codewords having corrected information symbols, at which time check symbols of the RS code may be discarded.