Highly degenerate quadratic forms over finite fields of characteristic 2

Authors:
Robert W. Fitzgerald
Affiliations:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA
Venue:
Finite Fields and Their Applications
Year:
2005

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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.