The maximum rank of 2×· · ·×2 tensors over F2

Publication Date

1-1-2021

Document Type

Article

Publication Title

Linear and Multilinear Algebra

Volume

69

Issue

3

DOI

10.1080/03081087.2020.1758019

First Page

394

Last Page

402

Abstract

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.).

Funding Sponsor

Social Sciences and Humanities Research Council of Canada

Keywords

computer algebra, finite fields, Multidimensional arrays, tensor rank

Department

Mathematics and Statistics

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