  This paper consists of two parts: (1) Using a Z[1/2]-form of Virasoro vertex
operator algebra L(1/2,0) with central charge 1/2, we obtain a modular vertex
operator algebra over any field F of finite characteristic different from 2. We
determine the generators and classify the irreducible modules for this vertex
operator algebra. (2) We investigate modular framed vertex operator algebras.
In particular, the rationality of modular framed vertex operator algebras is
established. For a modular code vertex operator algebra, the irreducible
modules are constructed and classified. Moreover, a Z[1/2]-form for any framed
vertex operator algebra over complex field C is constructed. As a result, one
can obtain a modular framed vertex operator algebra from any framed vertex
operator algebra over C.
