2012/06/22 by Murray R. Bremner, Bremner, Murray R., Jiaxiong Hu +1 · 1 citation
Computer Science · Engineering · Mathematics · #15A03 #15A21 #15A69 (Primary) 15-04 #15B33 #20G40 (Secondary) #Advanced MIMO Systems Optimization #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Tensor decomposition and applications #Wireless Communication Networks Research #math.AC #math.AG #math.CO #msc:15-04 #msc:15A03 #msc:15A21 #msc:15A69 #msc:15B33 #msc:20G40
paper · pdf · doi:10.48550/arxiv.1206.5179
13 pages, 10 tables
arxiv created 2012/06/22 · openalex publication_date 2012/06/22 · arxiv updated 2012/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider multidimensional arrays with at most 27 entries over the field with two elements, and their equivalence classes for the action of the direct product of general linear groups. The possible 3-dimensional formats are p x 2 x 2 (p = 2, ..., 6), p x 3 x 2 (p = 3, 4), and 3 x 3 x 3; the possible 4-dimensional formats are p x 2 x 2 x 2 (p = 2, 3). In each case, we compute the orbits for the group action, and then we determine the rank of each orbit. In particular, we determine the maximum rank for these arrays over F2.