On the solvability of systems of bilinear equations in finite fields

@article{Vinh2009OnTS,
  title={On the solvability of systems of bilinear equations in finite fields},
  author={L. Vinh},
  journal={arXiv: Combinatorics},
  year={2009}
}
  • L. Vinh
  • Published 2009
  • Mathematics
  • arXiv: Combinatorics
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 \[ B (\tmmathbf{a}_i, \tmmathbf{a}_j) = \lambda_{i j}, \tmmathbf{a}_i \in \mathcal{A}_i, i = 1, ..., k. \] We show that the system is solvable for any $\lambda_{i j} \in \mathbb{F}_q^{*}$, $1 \leq i,j \leq k$, given that the restricted sets $\mathcal{A}_i$'s are sufficiently large. 
4 Citations
Simplices over finite fields
  • 3
  • PDF
ON THE SOLVABILITY OF SYSTEMS OF SUM–PRODUCT EQUATIONS IN FINITE FIELDS
  • L. Vinh
  • Mathematics
  • Glasgow Mathematical Journal
  • 2011
  • 4
  • PDF

References

SHOWING 1-10 OF 30 REFERENCES
ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS
  • 30
  • PDF
Numbers of solutions of equations in finite fields
  • 567
  • PDF
...
1
2
3
...