 Gleason is also 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 duals that has become known as the MacWilliams identity . 
