Date of Award
Honors Thesis (Open Access)
Colby College. Mathematics and Statistics Dept.
In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and their success in creating a practical decoding process.
Gröbner Bases, Cyclic Codes, BCH Codes, Cooper's Philosophy, General Error Locator Polynomials
Recommended CitationSosa, Eduardo, "Decoding Cyclic Codes via Gröbner Bases" (2022). Honors Theses. Paper 1354.
Algebra Commons, Other Applied Mathematics Commons, Other Computer Sciences Commons, Other Mathematics Commons, Theory and Algorithms Commons