Analyzing Error Correcting Codes via Matroid Invariants

Midshipman Researcher(s): 1/C John Johnson

Adviser(s): Professor Max Wakefield

Poster #51

Error Correcting Codes (E.C.C.'s) are used to transmit data efficiently when errors in transmission can occur. Underlying each E.C.C. is a rich mathematical structure called a matroid. The aim of this project is to define and study methods to extract and condense specific numerical, topological, and algebraic information from a matroid. The methods we define are generalizations of the classical Mobius function in number theory and the chromatic polynomial in graph theory. We also examine topological representations of matroids and determine a close relationship between our methods and the well-known Betti numbers.

Full Size Mathematics #51