Summary: An \(r\)-ary symmetric channel has as transition probability matrix the \(r\times r\) matrix \(q_{xy}=p\) if \(x\neq y\) and \(q_{xy}= 1-(r- 1)p=q\) if \(x=y\). Given a set \(Y\) of \(r\) symbols, the code here consists of \(r\) codewords, each one of them made up of \(n\) identical symbols. Whenever \(q\) is larger than \(p\), maximum likelihood decoding amounts to finding out in the received vector which symbol is repeated most. Thus MLD here reduces to majority decoding. A generating function for the error probability as well as the probability of decoding failure for the system is obtained. Also recurrence relations are given for computing these probabilities. More generally, we consider a DMC (discrete memoryless channel) which we call transitive. An \(r\)-ary transitive DMC is a DMC such that there exists a transitive permutation group \(G\) on the set \(Y\) of symbols such that \(q_{xy}= q_{\sigma x,\sigma y}\) for all \((x,y)\in Y\times Y\) and for all \(\sigma\in G\). The results corresponding to those announced for the \(r\)-ary symmetric channel are obtained for the majority decoding repetition codes over \(r\)-ary transitive DMC. The construction of a Zinoviev like concatenation emphasizes the relevance of that mathematical model. We also prove in Section 5 that for every \(r\geq 3\) and \(n\), there exists a general DMC for which the repetition code of length \(n\) over \(r\) symbols is perfect for MLD.