The maximum rank of 2×· · ·×2 tensors over F2
Linear and Multilinear Algebra
We determine that the maximum rank of an order-n (Formula presented.) tensor with format (Formula presented.) over the finite field (Formula presented.) is (Formula presented.) for even n, and (Formula presented.) for odd n. Since tensor rank is non-increasing upon taking field extensions, (Formula presented.) gives the largest rank attainable for this tensor format. We also determine a maximum rank canonical form and compute its orbit under the action of the symmetry group (Formula presented.), and prove that this is the unique maximum rank canonical form, for even (Formula presented.).
Social Sciences and Humanities Research Council of Canada
computer algebra, finite fields, Multidimensional arrays, tensor rank
Mathematics and Statistics
Stavros Georgios Stavrou and Richard M. Low. "The maximum rank of 2×· · ·×2 tensors over F2" Linear and Multilinear Algebra (2021): 394-402. https://doi.org/10.1080/03081087.2020.1758019