#### Abstract

Let *K*/*F* be an extension of finite fields of characteristic two. We consider quadratic forms written as the trace of *x**R*(*x*), where *R*(*x*) is a linearized polynomial. We show all quadratic forms can be so written, in an essentially unique way. We classify those *R*, with coefficients 0 or 1, where the form has a codimension 2 radical. This is applied to maximal Artin-Schreier curves and factorizations of linearized polynomials.

paper-hideg.dvi (57 kB)

*.dvi copy*#### Recommended Citation

Fitzgerald, Robert W. "Highly Degenerate Quadratic Forms over Finite Fields of Characteristic 2." (Jan 2005).

## Comments

Published in

Finite Fields and Their Applications, 11, 165-181.