On the solvability of systems of bilinear equations in finite fields
| dc.creator | Vinh, Le Anh | |
| dc.date | 2009-03-06 | |
| dc.date.accessioned | 2026-07-07T12:49:50Z | |
| dc.date.available | 2026-07-07T12:49:50Z | |
| dc.description | Given $k$ 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.description | to appear in Proceedings of the American Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/0903.1156 | |
| dc.identifier | http://arxiv.org/abs/0903.1156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222508 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11L40, 11T30 | |
| dc.title | On the solvability of systems of bilinear equations in finite fields | |
| dc.type | text |