GALOIS EXTENSIONS AND SUBSPACES OF ALTERNATING BILINEAR FORMS WITH SPECIAL RANK PROPERTIES
By R. Gow, R. Quinlan. 2009
47 citations recorded by the source corpus.
Abstract Let K be a field admitting a cyclic Galois extension of degree n . The main result of this paper is a decomposition theorem for the space of alternating bilinear forms defined on a vector space of odd dimension n over K . We show that this space of forms is the direct sum of ( n - 1 ) / 2 subspaces, each of dimension n , and the non-zero elements in each subspace have constant rank defined in terms of the orders of the Galois automorphisms. Furthermore, if ordered correctly, for each integer k lying between 1 and ( n - 1 ) / 2 , the rank of any non-zero element in the sum of the first k subspaces is at most n - 2 k + 1 . Slightly less sharp similar results hold for cyclic extensions of even degree.
Subfields: Computational Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4401e5324b03a74c296997bca6a9fef4f16ee2ef
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Citations in the corpus
- New semifields and new MRD codes from skew polynomial rings (2018, unknown): “The sets Gk,σ were shown to be MRD codes for any cyclic Galois extension L in [19].”
- MRD Codes: Constructions and Connections (2019, background): “The following lemma, [40, Theorem 5], is key to the construction of the first and most well-known family MRD codes.”