In this paper, powerful induced-cyclic totally decom-posed cumulative Goppa (TDCG) codes are selected and used forcoded-cooperative diversity, which can fit wireless communicationapplications. Two TDCG codes employed at the source andrelay nodes establish the joint design of the destination channelcode. In the cooperation phase, we consider an optimized relaychannel code which improves the overall bit-error-rate (BER)performance. Two methods of optimization are explored. Themost practical method for optimization in terms of reducedprocessing complexity is proposed. We use a joint decodingwhich exploits all the resources gained by the cooperation schemeat the destination. The BER performance is evaluated throughMonte-Carlo simulations with BPSK modulation and coherentdetection over the flat Rayleigh fading channel. The proposedTDCG coded-cooperative diversity scheme exhibit a better BERperformance than the non-cooperation scheme and other existingcoded cooperation methods of similar code rates under similarchannel conditions.