  A $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated
to every symplectic involution on a central simple algebra of degree $8$ over a
field of characteristic $2$. The same construction on central simple algebras
of degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold
Pfister quadratic forms, and to every orthogonal involution a $1$-fold and a
$3$-fold quasi-Pfister forms. These forms hold structural information on the
algebra with involution.
