Codes and supersymmetry in one dimension

Abstract

Adinkras are diagrams that describe many useful supermultiplets in $D = 1$ dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology 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 $N = 32$.