Research Projects

This project aims to study and construct error-correcting codes for distributed storage, edge computing, network coding, and quantum computing. It will explore mathematical problems arising from technical challenges in smart telecommunications. The project will focus on linear codes associated to high-dimensional varieties and rank metric codes, as well as locally recoverable codes for distributed storage systems. The goal is to determine the trade-off between repair bandwidth and access, and design non-linear repair schemes for RS codes with general parameters. The project focuses on codes for multiple access channels, Reed-Muller codes for input-constrained discrete memoryless channels, optimal code construction for network coding and network function computation models, list decoding, improving distributed learning by Straggler mitigation, and quantum error-correcting codes. It aims to address the challenges of organizing mass access to a common source of communication, particularly in the context of mass mobile communications. The project also explores methods for constructing quantum error-correcting codes from classical algebraic codes over finite chain rings, and addresses the algorithmic aspects of encoding and decoding resulting QECCs.