  The sensitivity conjecture is a longstanding conjecture concerning the
relationship between the degree and sensitivity of a Boolean function. In 2015,
a communication game was formulated by Justin Gilmer, Michal Kouck\'{y}, and
Michael Saks to attempt to make progress on this conjecture. Andrew Drucker
independently formulated this game. Shortly after the creation of the GKS game,
Nisan Szegedy obtained a protocol for the game with a cost of $O(n^{.4732})$.
We improve Szegedy's result to a cost of $O(n^{.4696})$ by providing a
technique to identify whether a set of codewords can be used as a viable
strategy in this game.
