  Using the transfer matrix technique, we estimate the entropy for a gas of
rods of sizes equal to k (named k-mers), which cover completely a square
lattice. Our calculations were made considering three different constructions,
using periodical and helical boundary conditions. One of those constructions,
which we call Profile Method, was based on the calculations performed by Dhar
and Rajesh [Phys. Rev. E 103, 042130 (2021)] to obtain a lower limit to the
entropy of very large chains placed on the square lattice. This method, so far
as we know, was never used before to define the transfer matrix, but turned out
to be very useful, since it produces matrices with smaller dimensions than
those obtained using other approaches. Our results were obtained for chain
sizes ranging from k=2 to k=10 and they are compared with results already
available in the literature. In the case of dimers ($k=2$) our results are
compatible with the exact result, for trimers ($k=3$), recently investigated by
Ghosh et al [Phys. Rev. E 75, 011115 (2007)] also our results were compatible,
the same happening for the simulational estimates obtained by Pasinetti et al
[Physical Review E 104, 054136 (2021)] in the whole range of rod sizes. Our
results are consistent with the asymptotic expression for the behavior of the
entropy as a function of the size $k$, proposed by Dhar and Rajesh [Phys. Rev.
E 103, 042130 (2021)] for very large rods (k>>1).
