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This paper proposes a distributed RS coding scheme which is comprised of two different ReedSolomon (RS) codes over fast Rayleigh fading channel. Practically in any distributed coding scheme, an appropriate encoding strategy at the relay plays a vital role in achieving an optimized code at the destination. Therefore, the authors have proposed an efficient approach for proper selection of information at the relay based on subspace approach. Using this approach as the proper benchmark, another more practical selection approach with low complexity is also proposed. Monte Carlo simulations demonstrate that the distributed RS coding scheme under the two approaches can achieve nearly the same bit error rate (BER) performance. Furthermore, to jointly decode the source and relay codes at the destination, two different decoding algorithms named as naive and smart algorithms are proposed. The simulation results reveal that the advantage of smart algorithm as compared to naive one. The proposed distributed RS coding scheme with smart algorithm outperforms its non-cooperative scheme by a gain of 2.4-3.2 dB under identical conditions. Moreover, the proposed distributed RS coding scheme outperforms multiple existing distributed coding schemes, making it an excellent candidate for the future distributed coding wireless communications.