Title: Colorings of Hamming Graphs

 

Abstract: Error-correcting codes based on Hamming distance are a central topic of study in coding theory. Recent papers have used graphical representations of these codes (called Hamming Graphs) to allow their authors to reprove important coding theory results using tools from graph theory. A classical result exists which classifies all minimal colorings of a certain family of Hamming graphs. I will present original research proving an analogue of this result which applies to a larger class of Hamming graphs. 

 

No prior knowledge of coding theory (and only a rudimentary understanding of graph theory) is assumed.