  In 1982, Cameron and Liebler investigated certain "special sets of lines" in
PG(3,q), and gave several equivalent characterizations. Due to their
interesting geometric and algebraic properties, these "Cameron-Liebler line
classes" got a lot of attention. Several generalizations and variants have been
considered in the literature, the main directions being a variation of the
dimensions of the involved spaces, and studying the analogous situation in the
subset lattice. An important tool is the interpretation of the objects as
Boolean functions in the "Johnson" and "q-Johnson schemes".
  In this article, we develop a unified theory covering all these variations.
Generalized versions of algebraic and geometric properties will be
investigated, having a parallel in the notion of "designs" and "antidesigns" in
association schemes, which is connected to Delsarte's concept of
"design-orthogonality". This leads to a natural definition of the "degree" and
the "weights" of functions in the ambient scheme, refining the existing
definitions. We will study the effect of dualization and of elementary
modifications of the ambient space on the degree and the weights. Moreover, a
divisibility property of the sizes of Boolean functions of degree t will be
proven.
