Constructing 1-resilient rotation symmetric functions over $ {\mathbb F}_{p} $ with $ {q} $ variables through special orthogonal arrays

Jiao Du; Longjiang Qu; Chao Li; Xin Liao

doi:10.3934/amc.2020018

Article Contents

2020, Volume 14, Issue 2: 247-263. Doi: 10.3934/amc.2020018

This issue Previous Article Cyclic codes of length

$ 2p^n $

over finite chain rings Next Article Locally recoverable codes from algebraic curves with separated variables

Constructing 1-resilient rotation symmetric functions over $ {\mathbb F}_{p} $ with $ {q} $ variables through special orthogonal arrays

1.
Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang 453007, China
2.
College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
3.
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China

^* Corresponding author: Jiao Du([email protected])
^* Corresponding author: Jiao Du([email protected])

Received: May 2018

Revised: December 2018

Early access: September 2019

Published: May 2020

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Abstract

Based on the relation between resilient functions and large sets of orthogonal arrays, two classes of $ q $-variable 1-resilient rotation symmetric functions(RSFs) over $ {\mathbb F}_{p} $ are constructed. The first class of 1-resilient functions is obtained with the help of a Latin square with maximum cycle, and the second class of 1-resilient functions is constructed via switching the rotation symmetric orbits of the former class. Firstly, an efficient method to construct OA$ (pq, q, p, 1) $ is presented via solving a linear equation system. Secondly, we propose 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. In addition, two examples are given to demonstrate our constructions. It seems that the $ q $-variable 1-resilient RSFs constructed by our methods can not be constructed by earlier constructions.

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Mathematics Subject Classification: Primary: 05B15, 06E30; Secondary: 05E05, 94C10.

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