  The quantization of the complex linear superfield requires an infinite tower
of ghosts. Using the Batalin-Vilkovisky technique, Grisaru, Van Proeyen, and
Zanon have been able to define a correct procedure to construct a gauge-fixed
action. We generalize their technique by introducing the Lagrange multipliers
into the non-minimal sector and we study the characteristic BRST cohomology. We
show how the physical subspace is singled out. Finally, we quantize the model
in the presence of a background and of a quantum gauge superfield.
