Using codes for error correction and detection

Absiruct-A linear code C over GF( q) is good for t-error-correction and error detection if P(C, t; c) I P(C, t; (q 1)/q) for all z, 0 s c I (q 1)/q, where P( C, t; c) is the probability of an undetected error after a codeword in C is transmitted over a q-ary symmetric channel with error probability c and correction is performed for ail error patterns with t or fewer errors. A sufficient condition for a code to be good is derived. This sufficient condition is easy to check, and examples to illustrate the method are given.