# Build a Sporadic Group in Your Basement

by Paul E. Becker, Martin Derka, Sheridan Houghten, and Jennifer Ulrich

Year of Award: 2018

Publication Information: The American Mathematical Monthly, Volume 124, Number 4, April 2017, Pages 291-305.

Summary: Most finite simple groups fall into a few easy to understand categories, but there are a few sporadic (some might say "freakish") examples that defy easy classification. The Mathieu groups are the most accessible and applicable among these sporadic groups. With a lively and informative discussion of error-correcting codes, this article describes how the Mathieu groups connect to the extended Golay code. The authors give their readers a clear path of how different models of the Golay code connect together and give a way to use this to build the Mathieu groups in a simple and beautiful representation. (Note that no basements were harmed in the writing or reading of this paper.)

Response from the Authors:

It is a great honor to receive the MAA Paul R. Halmos-Lester R. Ford Award. We are very grateful for this recognition by the MAA. We are particularly pleased our paper was selected from the pages of American Mathematical Monthly, which consistently produces quality expository articles. We would like to thank the editor and referees, whose suggestions significantly improved the paper.

This article is a summary of a ten-year conversation between mathematicians and computer scientists. We set out to explore a specific question from coding theory. Our collaboration resulted in several narrowly-focused papers; this Monthly article is the other stuff. It is composed of ideas traded back-and-forth, translated through different viewpoints, and flavored by experiences along the way. Eventually, these different viewpoints became the most interesting aspect of our work.

We hope our paper encourages young mathematicians and computer scientists not only to develop a love for their respective fields, but also to pursue interdisciplinary problems. For inspiration, they could consider the question that led to our work: the (possible) existence of the length-72 extremal code. If such a code existed, it would be the third in an interesting sequence that starts with the extended Golay code.