Codes and Supersymmetry in One Dimension

Adinkras are diagrams that describe many useful supermultiplets in D = 1 di-mensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topol-ogy of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N = 28, and for minimal supermultiplets, up to N = 32. ar X i