Title of the talk: "Parameters of families of linear codes"

Date, Time & Venue: 25 August 2025  at 05 PM, Seminar Hall, Dept. of Mathematics

Abstract: Linear codes form a large family of error-correcting codes. Due to their algebraic properties, they are the most studied codes from the mathematical point of view. In this talk, we will be focusing on two families of linear codes and our work on determining their parameters. After reviewing the basics of linear codes, we will introduce a family of linear codes called toric codes over hypersimplices. These codes were defined by Jaramillo, Pinto and Villarreal in 2020. They determined the dimension and minimum distance of these codes. In this talk, we will discuss our work on computing the next-to-minimal weight of these codes using tools from Gr¨obner bases theory. Following this, we will discuss our work on the number of minimal weight codewords and next-to-minimal weight codewords of these toric codes. These are joint works with Prof. C´ ıcero Carvalho (UFU Brazil). Then we will discuss another parameter of linear codes called generalized Hamming weights. We will demonstrate how tools from Gr¨obner bases theory can also be used to determine the generalized Hamming weights of these codes. This is a joint work with my Ph.D. supervisor Dr. Sanjay Kumar Singh (IISER Bhopal). We will conclude this talk by discussing my other works in brief and potential future directions.

About the Speaker: Dr. Nupur Patanker is currently a Postdoctoral fellow (DST project) in the Department of Electrical Communication Engineering at IISc Bangalore. Her research area is Algebraic Coding Theory. She completed her Ph.D. in Mathematics from IISER Bhopal. She was an IoE-IISc Postdoctoral fellow in the Department of Electrical Communication Engineering at IISc Bangalore (February 2024-January 2025), Research Associate-III in the Department of Mathematics at IIT Jammu (June 2023-January 2024) and NBHM Postdoctoral fellow in the Department of Mathematics at IISER Pune (June 2021-May 2023).