Five Constructions of Permutation Polynomials over \gf(q²)

2015/11/01 by Cunsheng Ding, Pingzhi Yuan, Ding, Cunsheng +1 · 1 citation
Computer Science · Engineering · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.1511.00322

openalex publication_date 2015/11/01 · arxiv created 2015/11/11 · arxiv updated 2015/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Four recursive constructions of permutation polynomials over \gf(q²) with those over \gf(q) are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over \gf(q^{2^ℓ}) for any positive integer ℓ with any given permutation polynomial over \gf(q). A generic construction of permutation polynomials over \gf(2^2m) with o-polynomials over \gf(2^m) is also presented, and a number of new classes of permutation polynomials over \gf(2^2m) are obtained.

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