On the solvability of systems of bilinear equations in finite fields

dc.creatorVinh, Le Anh
dc.date2009-03-06
dc.date.accessioned2026-07-07T12:49:50Z
dc.date.available2026-07-07T12:49:50Z
dc.descriptionGiven $k$ sets $\mathcal{A}_i \subseteq \mathbb{F}_q^d$ and a non-degenerate bilinear form $B$ in $\mathbb{F}_q^d$. We consider the system of $l \leq \binom{k}{2}$ bilinear equations \[ B (\tmmathbf{a}_i, \tmmathbf{a}_j) = λ_{i j}, \tmmathbf{a}_i \in \mathcal{A}_i, i = 1, ..., k. \] We show that the system is solvable for any $λ_{i j} \in \mathbb{F}_q^{*}$, $1 \leq i,j \leq k$, given that the restricted sets $\mathcal{A}_i$'s are sufficiently large.
dc.descriptionto appear in Proceedings of the American Mathematical Society
dc.identifierhttps://arxiv.org/abs/0903.1156
dc.identifierhttp://arxiv.org/abs/0903.1156
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222508
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject11L40, 11T30
dc.titleOn the solvability of systems of bilinear equations in finite fields
dc.typetext

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