The undetected error probability threshold of m-out-of-n codes

The well-known m-out-of-n code /spl Omega//sub n//sup m/ consists of all binary vectors of length n and weight m. It is known that it is good for error detection (in the technical sense, that is, the probability of undetected error P/sub ud/(/spl Omega//sub n//sup m/,p)/spl les/P/sub ud/(/spl Omega//sub n//sup m/,1/2) for all p, 0/spl les/p/spl les/1/2) only for a few small values of m and n. It is therefore of interest to determine (bounds for) the threshold in general, that is, find the range of bit-error probabilities p for which P/sub ud/ (/spl Omega//sub n//sup m/,p)/spl les/P/sub ud/ (/spl Omega//sub n//sup m/,1/2). In this article such bounds are given.