2023/10/19 by Surajit Rajagopal, Rajagopal, S., P. Vanchinathan +1
Computer Science · Engineering · #11T06 #Coding theory and cryptography #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2310.12466
openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalising the concept of a complete permutation polynomial over a finite field, we define completness to level k for k≥1 in fields of odd characteristic. We construct two families of polynomials that satisfy the condition of high level completeness for all finite fields, and two more families complete to the maximum level a possible for large collection of finite fields. Under the binary operation of composition of functions one family of polynomials is an abelian group isomorphic to the additive group, while the other is isomorphic to the multiplicative group.