On the undetected error probability of binary expansions of Reed-Solomon codes
Kaiming Ho, Cyril Leung · IEEE Transactions on Information Theory · 1996
It has been shown by Kasami and Lin (see IEEE Trans. Commun., vol.32, p.998, 1984) that (n,k) Reed-Solomon codes used over a q-ary symmetric channel are proper. In this correspondence, it is shown that the binary expansions of these codes and their extensions, when used on the binary-symmetric channel, are not necessarily proper. In particular, certain codes of rate less than [1-log/sub 2/m+{(m-1)/m}log/sub 2/(m-1)] where m=log/sub 2/ q are not proper.