4,118 research outputs found
Codes and Supersymmetry in One Dimension
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.Comment: 48 pages, a new version that combines arXiv:0811.3410 and parts of
arXiv:0806.0050, for submission for publicatio
Computer classification of linear codes
We present algorithms for classification of linear codes over finite fields,
based on canonical augmentation and on lattice point enumeration. We apply
these algorithms to obtain classification results over fields with 2, 3 and 4
elements. We validate a correct implementation of the algorithms with known
classification results from the literature, which we partially extend to larger
ranges of parameters.Comment: 18 pages, 9 tables; this paper is a merge and extension of
arXiv:1907.10363 and arXiv:1912.0935
- …