Introduction to Set Shaping Theory

Abstract: In this article, we define the Set Shaping Theory whose goal is the study of the bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that meet this condition are many but since the goal of this theory is the transmission of data, we have analyzed the function that minimizes the average information content. The results obtained show how this type of function can be useful in data compression.