Permutation group codes originated in unpublished memos of David Slepian in the 1950's. These codes are derived by choosing a point on an n-dimensional sphere and acting on it with a group of operations consisting of permutations of the coordinates and reversals of the signs of coordinates.

The generalizations of permutation group codes have concentrated on using real reflection groups (Coxeter groups), which have a well-understood structure and action. The 1996 paper of Mittelholzer and Lahtonen is particularly comprehensive. These algorithms were refined recently by Fossorier, Nation and Peterson.

The group codes developed so far have used real reflection groups, operating on the unit sphere in a real vector space. Wes Peterson was always curious to know what other groups might have an action that lends itself well to coding. Now, we are developing group codes using complex permutation groups acting on the unit sphere in the complex plane and how well it works for encoding and decoding purposes.

As a fellow in 2009-10, Hye Jung partnered with Karl Higa at Noelani Elementary. She would also lead a team at the 2010 Math Olympics.

In 2010-11, Hye Jung would partner with Dara Lukonen at Akaʻula Elementary School on Molokaʻi. Her partnership here was integral in the developement of Molokaʻi Math Day, a now annual event with SUPER-M.

In 2011, Hye Jung would successfully defend and earn her Masters degree in Mathematics.