Classification of 9-dimensional trilinear alternating forms over GF(2) |
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| Institution: | 1. Department of Mathematics, Faculty of Engineering, Czech University of Life Sciences Prague, Kamýcká 129, 165 21, Prague, Czech Republic;2. Google Germany GmbH, Erika-Mann-Straße 33, 80636 München, Germany;1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet 303B, 2800 Kgs. Lyngby, Denmark;2. Department of Mathematics and Statistics, University of Tromsø, Hansine Hansens veg 18, 9019, Norway;1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, PR China;2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, PR China;3. Department of Mathematics, Ewha Womans University, Seoul, 03760, South Korea;1. Departamento de Matemáticas, Universidad de León, Spain;2. Departamento de Matemáticas, Universidad de Salamanca, Spain |
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| Abstract: | Let V be a finite-dimensional vector space over a finite field and let f be a trilinear alternating form over V. For such forms, we introduce two new invariants. Together with a generalized radical polynomial used for classification of forms in dimension 8 over GF(2), they are sufficient to distinguish between all trilinear alternating forms in dimension 9 over GF(2). To prove the completeness of the list of forms, we computed their groups of automorphisms. There are 31 degenerate and 317 nondegenerate forms. We point out some forms with either small or large automorphism group. |
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| Keywords: | Trilinear alternating form Radical polynomial Classification |
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