Permutation polynomials: iteration of shift and inversion maps over\n finite fields

2019/10/28 by Anna Chlopecki, Juliano Levier-Gomes, Chlopecki, Anna +7
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1910.12928

openalex publication_date 2019/10/28 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We show that all permutations in S_n can be generated by affine unicritical\npolynomials. We use the \PGL group structure to compute the\ncycle structure of permutations with low Carlitz rank. The tree structure of\nthe group generated by shift and inversion maps is used to study the randomness\nproperties of permutation polynomials.\n

Citations

• A monte carlo method for factorization

Related

• Specific permutation polynomials over finite fields
• A Representation of Permutations with Full Cycle
• Constructions and necessities of some permutation polynomials
• Further Results on Permutation Polynomials over Finite Fields
• Some permutation polynomials via linear translators