  This paper describes a fundamental correspondence between Boolean functions
and projection operators in Hilbert space. The correspondence is widely
applicable, and it is used in this paper to provide a common mathematical
framework for the design of both additive and non-additive quantum error
correcting codes. The new framework leads to the construction of a variety of
codes including an infinite class of codes that extend the original ((5,6,2))
code found by Rains [21]. It also extends to operator quantum error correcting
codes.
