Constructing 1-resilient rotation symmetric functions over \(\mathbb{F}_p\) with \(q\) variables through special orthogonal arrays (Q2176291)

In this paper, two classes of \(q\)-variable 1-resilient rotation symmetric functions (RSFs) over \(\mathbb{F}_p\) are constructed. This construction is based on the relation between resilient functions and large sets of orthogonal arrays. A generalized method of the known results proposed by \textit{J. Du} et al. [``New constructions of \(q\)-variable 1-resilient rotation symmetric functions over \({\mathbb F}_p\)'', Sci. China, Inf. Sci. 59, No. 7, Article ID 079102 (2016)] to obtain a class of \(q\)-variable 1-resilient RSFs was proved. The first class of 1-resilient functions is obtained with the help of a Latin square with maximum cycle structure, and the second class of 1-resilient functions is constructed via switching the rotation symmetric orbits of the former class. For this, an efficient method to construct \(\mathrm{OA}(pq; q; p; 1)\) is presented via solving a linear equation system. Secondly, some schemes to construct more \(q\)-variable 1-resilient RSFs by modifying the \(l\)-value support tables of the known \(q\)-variable 1-resilient RSFs were proposed. In addition, two examples are given to demonstrate their constructions. The construction of 1-resilient RSFs on given number of variables remains an open problem.