Using codes for error correction and detection (Corresp.)
Torleiv Kløve · IEEE Transactions on Information Theory · 1984
A linear codeCover GF(q)is good fort-error-correction and error detection ifP(C,t;\epsilon) \leq P(C,t;(q - 1)/q)for all\epsilon, 0 \leq \epsilon \leq (q - 1)/q, whereP(C, t; \epsilon)is the probability of an undetected error after a codeword inCis transmitted over aq-ary symmetric channel with error probability\epsilonand correction is performed for all error patterns withtor 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.