Real MDS Codes for Error Correction: Construction and an Application on Federated Learning Pre Aggregation Validation

Real number codes play a crucial role in correcting errors within communication systems that involve the transmission of analog signals or continuous data. Among these codes, Maximum Distance Separable (MDS) codes stand out as highly efficient for error correction. The present research paper is on the construction of a class of real number MDS codes for any desired dimension. The main objective is to enhance the error-detection and correction capability of a communication system through the application of a real-number code which has the maximum distance and hence the maximum error-detection and correction capability. The paper introduces a practical and systematic approach for encoding and decoding of messages which are in the form of real arrays using the proposed real MDS code. Also, an application of a real MDS code in federated learning is provided and illustrated with a case study.