The growing number of Internet of Thing (IoT) and Ultra-Reliable Low Latency Communications (URLCC) use cases in next generation communication networks calls for the development of efficient Forward Error Correction (FEC) mechanisms. These use cases usually imply using short to mid-sized information blocks and requires low-complexity and/or fast decoding procedures. This paper investigates the joint learning of short to mid block-length coding schemes and associated Belief-Propagation (BP) like decoders using Machine Learning (ML) techniques. An interpretable auto-encoder (AE) architecture is proposed, ensuring scalability to block sizes currently challenging for ML-based linear block code design approaches. By optimizing a coding scheme w.r.t. the targeted decoder, the proposed system offers a good complexity/performance trade-off compared to various codes from literature with length up to 128 bits.