Highly Degenerate Quadratic Forms over Finite Fields of Characteristic 2

Authors

Robert W. Fitzgerald, Southern Illinois University CarbondaleFollow

Comments

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

Abstract

Let K/F be an extension of finite fields of characteristic two. We consider quadratic forms written as the trace of xR(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.

Recommended Citation

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