Algorithm for the generation of complement-free sets

Fülöp, Dániel and Hannusch, Carolin (2019) Algorithm for the generation of complement-free sets. Annales Mathematicae et Informaticae, 50. pp. 89-92. ISSN 1787-5021 (Print), 1787-6117 (Online)

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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.

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