The Power of Algebraic Curves: Advancing Error Correcting Codes in Coding Theory

Raviraju Balappa D, Dr. Gautam Kumar Rajput

Abstract: This study investigates the intersection of algebraic geometry and coding theory, specifically focusing on the application of algebraic curves in the advancement of error-correcting codes. Algebraic curves, as mathematical objects, offer profound implications in the design and analysis of error-correcting codes, providing robust solutions to the challenges of data transmission and storage. This paper delves into the theoretical foundations of algebraic curves, their role in constructing powerful error-correcting codes, and the practical applications of these codes in various technological domains.

Keywords: Algebraic Geometry, Error-Correcting Codes, Algebraic Curves, Goppa Codes, Finite Fields