Upper and lower bounds on the undetected error probability of binary codes derived from shortened Reed-Solomon codes

The number of codewords with small weights is investigated for the binary codes derived from shortened Reed-Solomon codes. A formula is shown for the exact number of codewords with weight 2 in the binary image of a shortened Reed-Solomon code generated by (X- alpha ). This number does not depend on the choice of the primitive element alpha . Upper bounds on the number of codewords with small weights are also derived for the binary image of a shortened code generated by (X- alpha ) and (X-1)(X- alpha ) by using the relation between the Reed-Solomon code and Hamming code. The number of codewords with the minimum weight is also discussed for the binary images of other Reed-Solomon codes. By using the results, the undetected error probability is evaluated.<
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