Research Projects

Algebraic families of error correcting codes like Reed-solomon codes, Reed-Muller codes, Multiplicity codes and BCH codes form an important and extremely well studied area in coding theory. In this project, we aim to study certain fundamental computational questions about the algorithmic decodability of these families of codes. In particular, (i) Researchers aim to understand the question of algorithmic decoding of multivariate polynomial evaluation codes like Reed-Muller and Multivariate Multiplicity codes over arbitrary product sets and arbitrary fields, (i) explicit construction of Reed-solomon codes that are combinatorially list decodable beyond the Johnson radius, and designing efficient algorithms to decode them in this regime of parameters, and (iii) to understand if the improvement on the above questions has implications in releated areas like complexity theory and pseudorandomness.