Roth-Karp decomposition is a classical functional decomposition technique; because it can decompose a node into a set of nodes with fewer numbers of fanins, it is one of the most popular techniques for look-up table (LUT)-based field-programmable gate array technology mapping. The compatible-class encoding problem in Roth-Karp decompositions is discussed in the paper. It is shown how to formulate this problem as a symbolic-output encoding problem to exploit the feature of the two-output LUT architecture specifically. Based on this formulation an encoding algorithm is developed to minimise the number of LUTs used to implement the logic circuit. Experimental results show that the encoding algorithm can produce promising results to implement boolean networks in the logic synthesis environment for the two-output LUT architecture.