Algorithm for the generation of complement-free sets

Abstract

We introduce an algorithm for the generation of complement-free sets of binary 𝑚 -tuples, where 𝑚 is even. We also provide an implementation for this algorithm for 𝑚 = 12 . Such complement-free sets are needed for the generation of a new class of error-correcting codes, which were introduced by Hannusch and Lakatos. These codes build the fundamental improvement in the cryptographic system of Dömösi, Hannusch and Horváth. Therefore the generation of complement-free sets will be important for cryptographic applications. In the end of the paper we give some interesting facts about complement-free sets as combinatorial objects.