= Reed-Solomon error correction
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{title2=$\operatorname{RS}_k(a_1,\ldots,a_n)$}
{wiki=Reed–Solomon_error_correction}
= Reed-Solomon code
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= RS code
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For distinct elements $a_1,\ldots,a_n$ of a <finite field>, a Reed-Solomon code consists of the evaluation vectors $(f(a_1),\ldots,f(a_n))$ of <polynomials> with degree less than $k$. It has <dimension> $k$ and <minimum Hamming distance> $n-k+1$, 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>.
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