Highly degenerate quadratic forms over F2

Authors:
Robert W. Fitzgerald
Affiliations:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA
Venue:
Finite Fields and Their Applications
Year:
2007

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Highly degenerate quadratic forms over finite fields of characteristic 2

Finite Fields and Their Applications

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Abstract

Let K be a finite extension of F"2. We consider quadratic forms written as the trace of xR(x), where R(x) is a linearized polynomial. We determine the K and R(x) where the form has a radical of codimension 2. This is applied to constructing maximal Artin-Schreier curves.