Most real world data sets consist of data vectors whose individual components are not statistically independent. In other words, knowing the value of an element will provide information about the value of elements in the data vector. When this occurs, it can be desirable to create a factorial code of the data, i. e., a new vector-valued representation of each data vector such that it gets uniquely encoded by the resulting code vector (loss-free coding), but the code components are statistically independent.