Preface: Special functions and codes

Excerpt

In the past two decades, we have witnessed a lot of interplays between special functions and codes. In one direction, special codes were employed to construct functions with desirable properties. A very successful example in this direction is the Carlet-Feng construction of an infinite family of balanced Boolean functions having good cryptographic properties with the Reed-Solomon codes (see, Proceedings of ASIACRYPT 2008, LNCS 5350, pp. 425–440, 2008, Springer Verlag). The BCH bound plays an important role in proving the degree of the algebraic immunity of the Carlet-Feng family of Boolean functions. In the other direction, many special functions were used in different ways for constructing optimal linear codes. For instance, almost perfect nonlinear functions, planar functions and Dickson polynomials were employed to produce optimal linear codes in many references. These nice and impressive interplays between special functions and codes are the driving force of this special issue, which includes ten rigorously selected papers from the original submissions. …