Let r≥3 be a positive integer and Fq 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 Fqd and σM is an invertible linear map over Fqd. 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)).
吴霞，东南大学金沙威尼斯欢乐娱人城副教授，博士生导师。博士毕业于南京大学数学系。目前研究方向是代数K理论和代数编码。主持国家自然科学基金面上项目一项，青年基金一项; 国家博士后基金特别资助一项，面上项目一项。在Ramanujan，Acta Arith.，DCC，FFA等期刊发表SCI论文10余篇。
