An analogue of Vosper's theorem for extension fields

DOI10.1017/S0305004117000044zbMath1405.11134arXiv1501.00602MaRDI QIDQ5372073

Oriol Serra, Christine Bachoc, Gilles Zémor

Publication date: 24 October 2017

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00602

zbMATH Keywords

field extensionVosper's theorem\(F\)-linear subspaces

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Separable extensions, Galois theory (12F10) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

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Cites Work

• Plünnecke and Kneser type theorems for dimension estimates
• Symmetric bilinear forms over finite fields with applications to coding theory
• On the sum of two sets in a group
• Summenmengen in lokalkompakten abelschen Gruppen
• Eigenvalues of association schemes of quadratic forms
• Some additive applications of the isoperimetric approach
• Alternating bilinear forms over GF(q)
• Bilinear forms over a finite field, with applications to coding theory
• Revisiting Kneser's theorem for field extensions
• A generalization of an addition theorem of Kneser.
• Association schemes of quadratic forms and symmetric bilinear forms
• An isoperimetric method in additive theory
• Symmetric bilinear forms over finite fields of even characteristic
• On the connectivity of Cayley digraphs
• Yahya Ould Hamidoune's mathematical journey: a critical review of his work
• The Critical Pairs of Subsets of a Group of Prime Order
• On linear versions of some addition theorems
• Some results in additive number theory I: The critical pair theory
• Association schemes and coding theory
• Number of Points of Varieties in Finite Fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item