Linear codes and incidence structures of bent functions and their generalizations

DOI10.1016/J.DISC.2022.113157arXiv2012.06866WikidataQ114190447 ScholiaQ114190447MaRDI QIDQ6355908

Alexander Pott, Alexandr A. Polujan, Wilfried Meidl

Publication date: 12 December 2020

Abstract: In this paper we consider further applications of $(n,m)$-functions for the construction of 2-designs. For instance, we provide a new application of the extended Assmus-Mattson theorem, by showing that linear codes of APN functions with the classical Walsh spectrum support 2-designs. On the other hand, we use linear codes and combinatorial designs in order to study important properties of $(n,m)$-functions. In particular, we give a new design-theoretic characterization of $(n,m)$-plateaued and $(n,m)$-bent functions and provide a coding-theoretic as well as a design-theoretic interpretation of the extendability problem for $(n,m)$-bent functions.

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Boolean functions (94D10)

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