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 topologyof 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. © 2011 International Press.