2022/12/25 by Wei Lu, Xia Wu, Lu, Wei +5
Computer Science · Engineering · Mathematics · #94A62 #94B05 #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2212.12869
openalex publication_date 2022/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let r≥ 3 be a positive integer and \mathbbFq the finite field with q elements. In this paper, we consider the r-regular complete permutation property of maps with the form f=τ∘σM∘τ-1 where τ is a PP over an extension field \mathbbFqd and σM is an invertible linear map over \mathbbFqd. We give a general construction of r-regular PPs for any positive integer r. When τ is additive, we give a general construction of r-regular CPPs for any positive integer r. When τ is not additive, we give many examples of regular CPPs over the extension fields for r=3,4,5,6,7 and for arbitrary odd positive integer r. These examples are the generalization of the first class of r-regular CPPs constructed by Xu, Zeng and Zhang (Des. Codes Cryptogr. 90, 545-575 (2022)).