In the investigation of relationship between the periodicity of fitness function and encoding cardinality, the evaluation of encoding performance using the number of order-1 building blocks is not necessarily established. Focused on this issue, evaluating method of encoding performance of Genetic Algorithm (GA) using Accumulated Escape Probability (AEP) was proposed, and for a class of fitness functions linearly combined of sinusoidal functions whose frequencies are exponential to a positive integer m, research on encoding was carried out. Firstly, the general form of the fitness function was given, and the concept of base- m encoding was explained. Secondly, the definition of AEP was introduced, and a method was proposed to figure out AEPs. Then the AEPs of the above-mentioned fitness functions under encodings with different encoding bases were compared, and the results showed that, for a fitness function which was linearly combined of sinusoidal functions with frequencies exponential to a positive integer m, a base- m encoding could achieve higher AEP than encodings with bases other than m. The simulation results show that, the optimization performance and the rise time of the average fitness of the population under a base- m encoding are significantly better than those of the other encodings.