Algebraic Analysis of The Encoding and Decoding Process of Goppa Code with Implementation in SageMath - Rahwanto, Taufiq Hamid; Utomo, Putranto Hadi; Siswanto (Universitas Brawijaya, 2026)
Error-Correcting Code (ECC) is one of the solutions that have been widely developed to overcome errors, with the aim of detecting and correcting errors that occur. Among the various types of ECC, Goppa code have proven to be effective in maintaining data integrity. This study focuses on examining how the algebraic structure of the Goppa code is utilized for ECC, thereby enabling an understanding of how elements in the field can be transformed into binary vectors and polynomials to construct the parity-check matrix and the generator matrix. The algebraic structure is then analyzed to determine whether it can be optimized to detect and correct errors in the encoding and decoding processes. Subsequently, a simple program will be developed using the SageMath programming language, followed by simulations. The simulation results are expected to optimize the error-correction capacity, thereby demonstrating an improvement in the error-correction capability of the Goppa code during the decoding process.