values have been found. In the same 1955 paper, Greenwood and Gleason also computed the multicolor Ramsey number R(3,3,3): the smallest number r such that, if a complete graph on r vertices has its edges colored with three colors, then it necessarily contains a monochromatic triangle. As they showed, R(3,3,3) = 17; this remains the only nontrivial multicolor Ramsey number whose exact value is known. As part of their proof, they used an algebraic construction to show that a 16-vertex complete graph can be decomposed into three disjoint copies of a triangle-free 5-regular graph with 16 vertices and 40 edges<ref name="spencer-dm">. </ref> (sometimes called the Greenwood–Gleason graph). Ronald Graham writes that the paper by Greenwood and Gleason "is now recognized as a classic in the development of Ramsey theory". In the late 1960s, Gleason became the doctoral advisor of Joel Spencer, who also became known for his contributions to Ramsey theory.<ref name="mathgenealogy"> </ref> Coding theory Gleason published few contributions to coding theory, but they were influential ones, and included "many of the seminal ideas and early results" in algebraic coding theory. During the 1950s and 1960s, he attended monthly meetings on coding theory with Vera Pless and others at the Air Force Cambridge Research Laboratory. Pless, who had previously worked in abstract algebra but became one of the world's leading experts in coding theory during this time, writes that "these monthly meetings were what I lived for." She frequently posed her mathematical problems to Gleason and was often rewarded with a quick and insightful response. The Gleason–Prange theorem is named after Gleason's work with AFCRL researcher Eugene Prange; it was originally published in a 1964 AFCRL research report by H. F. Mattson Jr. and E. F. Assmus Jr. It concerns the quadratic residue code of order n, extended by adding a single parity check bit. This "remarkable theorem" shows that this code is highly symmetric, having the projective linear group PSL2(n) as a subgroup of its symmetries. Gleason is the namesake of the Gleason polynomials, a system of polynomials that generate the weight enumerators of linear codes. These polynomials take a particularly simple form for self-dual codes: in this case there are just two of them, the two bivariate polynomials x2 + y2 and x8 + 14x2y2 + y8. Gleason's student Jessie MacWilliams continued Gleason's work in this area, proving a relationship between the weight enumerators of codes and their