A New Characterization of 2-Resilient Rotation Symmetric Boolean Functions

Abstract

In this paper, the notion of 2-tuples distribution matrices of the rotation symmetric orbits is proposed, by using the properties of the 2-tuples distribution matrix, a new characterization of 2-resilient rotation symmetric Boolean functions is demonstrated. Based on the new characterization of 2-resilient rotation symmetric Boolean functions, constructions of 2-resilient rotation symmetric Boolean functions(RSBFs) are further studied, and new 2-resilient rotation symmetric Boolean functions with prime variables are constructed.

Constructions of 2-Correlation Immune Rotation Symmetric Boolean Functions

“…In this paper, O n (x) also represents the following orbit matrix when no confusion can arise [12][13][14][15],…”

“…In 2020, Du et al [13] proposed the concept of 2-tuples distribution matrix of the rotation symmetric orbits, and then constructed a class of 2-resilient RSBFs with 4t − 1 variables. Recently, Du et al [14] proposed a new characterization of 2-resilient RSBFs by the 2-tuples distribution matrix. So far as we know, there are few results about 2-CI RSBFs.…”

Constructions of optimal 2-level orthogonal arrays with repeated rows

“…In [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], several proofs of the Plackett-Burman bound are provided, a desired inequality for orthogonal arrays of strength two containing repeated rows is also presented, and some of these proofs are studied that can be strengthened to yield the aforementioned bound for OAs of strength two with repeated rows. A general result of the desired inequality for orthogonal arrays of strength t containing repeated rows was proposed in [2,17].…”