On the decoder error probability for Reed - Solomon codes (Corresp.)

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
t
error-correcting Reed-Solomon code of length
q - 1
over GF
(q)
, if more than
t
errors occur, the probability of decoder error is less than
1/t!
.