Description
Title: Generalized Hamming weights of (projective) Reed-Muller codes.
Abstract: Reed-Muller codes are among the most elementary and most studied codes. Less studied, but equally elementary are their projective counterparts, the protective Reed-Muller codes. Many open questions remain about these codes. Mathematically, a very interesting question is the determination of the generalized Hamming weights. The determination of these weights is equivalent to the determination of the maximum number of common solutions to certain system of polynomial equations. In this talk, I will give an overview of recent work and developments on the theory of generalized Hamming weights of projective Reed-Muller codes. This work was carried out together with Mrinmoy Datta and Sudhir Ghorpade.