A class of functions and their application in constructing semisymmetric designs

The article delves into the mathematical properties of a specific class of functions known as semiplanar functions of index. These functions are utilized to construct semisymmetric designs (SSDs), which are crucial in the field of combinatorial design theory. The research builds on previous work on planar functions and differential uniformity, extending these concepts to more general cases. The main results include the establishment of conditions under which certain functions lead to SSDs and the exploration of the connectedness of these designs. Additionally, the paper provides a detailed examination of the existence and construction of semiplanar functions over finite fields, highlighting their significance in both theoretical and practical aspects of cryptography and design theory.