  In this work we have considered formal power series and partial differential
equations, and their relationship with Coding Theory. We have obtained the
nature of solutions for the partial differential equations for Cycle Poisson
Case. The coefficients for this case have been simulated, and the high tendency
of growth is shown. In the light of Complex Analysis, the Hadamard
Multiplication's Theorem is presented as a new approach to divide the power
sums relating to the error probability, each part of which can be analyzed
later.
