Codes for error detection, good or not good

Linear codes for error detection on a q-ary symmetric channel are studied. It is shown that for given dimension k and minimum distance d, there exists a value /spl mu/(d, k) such that if C is a code of length n /spl ges/ /spl mu/(d,k), then neither C nor its dual C/sup /spl perp// are good for error detection. For d /spl Gt/ k or k /spl Gt/ d good approximations for /spl mu/(d, k) are given. A generalization to nonlinear codes is also given.