Necessities and sufficiencies of a class of permutation polynomials over finite fields

2019/07/28 by Xiaogang Liu, Liu, Xiaogang
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1907.12086

openalex publication_date 2019/07/28 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28

Abstract

For the finite field \mathbbF_2^3m, permutation polynomials of the form (x^2m+x+δ)^s+cx are studied. Necessary and sufficient conditions are given for the polynomials to be permutation polynomials. For this, the structures and properties of the field elements are analyzed.

Citations

• Further results on some classes of permutation polynomials over finite fields
• Permutation polynomials and group permutation polynomials

Related

• Constructions and necessities of some permutation polynomials
• A general construction of permutation polynomials of the form (x^2m+x+δ)^i(2m-1)+1+x over \F_2^2m
• New classes of permutation polynomials with coefficients 1 over finite fields
• More new classes of permutation trinomials over \mathbbF_2ⁿ
• Further results on some classes of permutation polynomials over finite fields