  Calculation of the Shannon information entropy (S) and its connection with
the order-disorder transition, and with inter-particle interaction provide a
challenging research area in the field of quantum information. Experimental
progress with cold trapped atoms has corroborated this interest. In the present
work, S is calculated for the Bose-Einstein condensate (BEC) with dominant
dipolar interaction for different dipole strengths, trap aspect ratio and
number of particles (N). Trapped dipolar bosons in an anisotropic trap provide
an example of system where the effective interaction is strongly determined by
the trap geometry. The main conlcusion of the present calculation is that the
anisotropic trap reduces the number of degrees of freedom, resulting in more
ordered configurations. The Landsberg's order parameter exhibits quick
saturation with the increase in scattering length in both prolate and oblate
traps. We also define the threshold scattering length which makes the system
completely disordered. Unlike non-dipolar BEC in a spherical trap, we do not
find a universal linear relation between S and ln N, and we, therefore,
introduce a general quintic polynomial fit rather well working for a wide range
of particle number.
