  Planar functions in odd characteristic were introduced by Dembowski and
Ostrom in order to construct finite projective planes in 1968. They were also
used in the constructions of DES-like iterated ciphers, error-correcting codes,
and signal sets. Recently, a new notion of pseudo-planar functions in even
characteristic was proposed by Zhou. These new pseudo-planar functions, as an
analogue of planar functions in odd characteristic, also bring about finite
projective planes. There are three known infinite families of pseudo-planar
monomial functions constructed by Schmidt and Zhou, and Scherr and Zieve. In
this paper, three new classes of pseudo-planar binomials are provided.
Moreover, we find that each pseudo-planar function gives an association scheme
which is defined on a Galois ring.
