Reed–Solomon error correction is a type of error-correcting code that is widely used in digital communications and data storage systems to detect and correct errors in data. It is named after Irving S. Reed and Gustave Solomon, who developed the code in the 1960s. ### Key Features of Reed-Solomon Codes: 1. **Block Code**: Reed-Solomon codes operate on blocks of symbols, rather than on individual bits.
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For distinct elements of a finite field, a Reed-Solomon code consists of the evaluation vectors of polynomials with degree less than . It has dimension and minimum Hamming distance , so it is a maximum distance separable code. A nonzero polynomial has at most its degree many distinct polynomial roots. Primitive cyclic Reed-Solomon codes use all nonzero field elements, ordered as powers of a primitive root of unity; arbitrary evaluation sets need not give a cyclic code.