Reed–Solomon or RS(n, k) codes are nonbinary cyclic codes composed of sequences of symbols of m-bits, where m > 2 is an integer, which exist for all n and k, 0 < k < n < 2m + 2. In this notation, n is the total number of code symbols in an encoded block (usually called length), and k is the number of data symbols to be encoded. Generally, (n, k) = (2m − 1, 2m − 1 − 2t), where t is the (symbol) error correcting capability of the code. An extended RS code can have n = 2m or n = 2m + 1. Among all linear codes with the same encoding input and output block lengths, RS codes have the largest possible minimum distance. Similar to the Hamming distance, the distance between two codewords in a nonbinary code is defined ...
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