Erasure codes can generate data redundancy in distributed storage systems. This redundancy can be used to recover missing data in case of a failure. Codes have the benefit of reducing the generated amount of redundancy drastically,compared to plain data replication. However, this reduction is combined with a significant computational complexity, which penalizes encoding and decoding performances, and limits the use of coding to cold data. In this thesis, we focus on the use of the Mojette transform as an effective erasure code, adapted to hot data. The resulting code requires more redundancy than classical codes though. The first contribution of this research work deals with the design of a systematic version of the Mojette erasure code. This version provides better performances while reducing the required amount of redundancy. The second contribution covers the integration of this solution in the distributed file system RozoFS. This integration enables the system to provide a continuous service despite failures, while being able to manage hot data with half the volume of data compared to replication-based systems. A third research focus addresses the design of a distributed method to compute extra Mojette codeword symbols. This method contributes to restore a redundancy threshold in the storage system.