Digital Communications: Fundamentals and Applications, 3rd Edition

7.6 Reed–Solomon Codes

Reed–Solomon (R–S) codes are nonbinary cyclic codes with symbols made up of m-bit sequences, where m is any positive integer having a value greater than 2. R–S (n, k) codes on m-bit symbols exist for all n and k for which

0<k<n<2m+2(7.24)

where k is the number of data symbols being encoded, and n is the total number of code symbols in the encoded block. For the most conventional R–S (n, k) code,

(n,k)=(2m−1,2m−1−2t)(7.25)

where t is the symbol-error-correcting capability of the code, and n − k = 2t is the number of parity symbols. An extended R–S code can be made up with n = 2m or n = 2m + 1 but not any further.

R–S codes achieve the largest possible code minimum distance for any linear code with the same encoder ...