Upper bounds On the decoder error probability for Reed-Solomon codes are derived. By definition, "decoder error" occurs when the decoder finds a codeword other than the transitted codeword; this is in contrast to "decoder failure," which occurs when the decoder fails to find any codeword at all. These results imply, for example, that for a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> error-correcting Reed-Solomon code of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q - 1</tex> over GF <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(q)</tex> , if more than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> errors occur, the probability of decoder error is less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/t!</tex> .
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McEliece et al. (1986) studied this question.