  We have studied the statistical and polarization properties of giant pulses
(GPs) emitted by the millisecond pulsar B1937+21, with high sensitivity and
time resolution. The observations were made in June 2005 with the 100-m Robert
C. Byrd Green Bank Telescope at S-band (2052-2116 MHz) using the Mk5A VLBI
recording system, with formal time resolution of 16 ns. The total observing
time was about 4.5 hours; the rate of detection of GPs was about 130 per hour
at the average longitudes of the main pulse (MPGPs) and 60 per hour at the
interpulse (IPGPs). While the average profile shows well-defined polarization
behavior, with regular evolution of the linear polarization position angle
(PA), GPs exhibit random properties, occasionally having high linear or
circular polarization. Neither MPGPs nor IPGPs show a preferred PA. The
cumulative probability distribution (CPD) of GP pulse energy was constructed
down to the level where GPs merge with regular pulses and noise. For both MPGPs
and IPGPs, the CPD follows a power law with a break, the power index changing
from -2.4 at high energy to -1.6 for low energy. Pulse smearing due to
scattering masks the intrinsic shape and duration of the detected GPs. The
smearing time varied during the observing session within a range of a few
hundred nanoseconds. The measured polarization and statistical properties of
GPs impose strong constraints on physical models of GPs. Some of these
properties support a model in which GPs are generated by the electric discharge
caused by magnetic reconnection of field lines connecting the opposite magnetic
poles of a neutron star.
