## 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.

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