Turkish Journal of Mathematics
DOI
10.3906/mat-1612-20
Abstract
Let $h, h_M: \mathbb {F} _q^n\to \mathbb {F} _q$ be quadratic forms with $h$ not degenerate. Fix $k\in \mathbb {F} _q$ and set $C_n(k,h)_{\mathbb {F} _q}:= \{h(x_1,\dots ,x_n)=k\}\subset \mathbb {F}_q^n$. We compute (in many cases) the image of $h_{M C_n(k,h)_{\mathbb {F} _q}}$. This question is related to a question on the numerical range of matrices over a finite field.
Keywords
Quadratic form, finite field
First Page
1
Last Page
11
Recommended Citation
BALLICO, EDOARDO
(2018)
"Restriction of a quadratic form over a finite field to a nondegenerate affine quadric hypersurface,"
Turkish Journal of Mathematics: Vol. 42:
No.
1, Article 1.
https://doi.org/10.3906/mat-1612-20
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss1/1
