Classifying Quadratic Forms Over Z2 in Four Variables
Amrita Acharyya
Department of Mathematics, University of Toledo Toledo, OH 43606, U.S.A
Gerard Thompson *
Department of Mathematics, University of Toledo Toledo, OH 43606, U.S.A
*Author to whom correspondence should be addressed.
Abstract
Quadratic forms in four variables over the field 
2 are sorted first of all with respect to permutation symmetry. Thereafter it is shown that any such form is equivalent to one of seven such canonical forms. The orthogonal group of each one of these seven forms is obtained. The paper closes with some remarks about quadratic forms in three variables.
Keywords: Quadratic form, field of two elements, orthogonal group