New formula to calculate the number of designs in RADG cryptosystem

Reaction automata direct graph (RADG) is a new technique that uses the automata direct graph method to represent a certain design for encryption and decryption. Jump states are available in the RADG design that enables the encipher to generate different ciphertexts each time from the same plaintext and wherein not a single ciphertext is related to a certain plaintext. This study created a matrix representation for RADG designs that allows the calculation of the number of cases ($F_{Q}$)mathematically possible for any design of the set $Q$. $F_{Q}$ is an important part of the function $mathrm{F}(mathrm{n}, mathrm{m}, lambda)$ that calculates the total number of cases of a certain design for the values $Q, R, sum, psi, J$ and $T$. This paper produces a mathematical equation to calculate $F_{Q}$.