Title of the talk: Quantum Codes Construction from Skew Cyclic Codes

Date , Time & Venue: 10 Oct. 2025  at 05 PM on  Dept. of Mathematics

Abstract: In this talk, we study skew cyclic codes over mixed alphabets. First, I will discuss some basics and my other related works. To characterise skew cyclic codes over the mixed alphabet, we first establish their algebraic structure and then consider an inner product to discuss the dual containing properties of these codes. Further, we define a Gray map over $\mathbb{F}_q\mathcal{R}$ and obtain their $\mathbb{F}_q$-Gray images. As an application, we apply the CSS (Calderbank-Shor-Steane) construction on Gray images of dual containing skew cyclic codes  and obtain many quantum codes with better parameters than the best-known codes available in the literature. I will conclude this talk by considering some future directions.

About the Speaker: Dr. Shikha Patel is currently working as an Assistant Professor in the Department of Mathematics at IIIT Bhopal, India (July 2025-Present). Before joining IIIT Bhopal,  she was a postdoctoral fellow at ETIS Lab, CNRS, France (November 2024- June 2025). Previously, she was an IoE-Postdoctoral Fellow in the Department of Electronic Systems Engineering at IISc Bangalore, India (September 2023-October 2024). Her research interest includes linear error-correcting ( skew cyclic, skew constacyclic, skew polycyclic) codes over finite commutative and non-commutative rings, quantum codes from classical codes, codes over mixed alphabets, etc. She worked on the linear codes over skew polynomial rings with both automorphisms and derivations and their applications in quantum error-correcting codes.