On the solvability of systems of bilinear equations in finite fields

Details On the solvability of systems of bilinear equations in finite fields On the solvability of systems of bilinear equations in finite fields

2009-03-06

arxiv.org/abs/0903.1156v1

Mathematics

Combinatorics

to appear in Proceedings of the American Mathematical Society

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the solvability of systems of bilinear equations in finite fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the solvability of systems of bilinear equations in finite fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the solvability of systems of bilinear equations in finite fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135693