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)).
吳霞，東南大學(xué)kaiyun開云官方網(wǎng)站副教授，博士生導(dǎo)師。博士畢業(yè)于南京大學(xué)數(shù)學(xué)系。目前研究方向是代數(shù)K理論和代數(shù)編碼。主持國家自然科學(xué)基金面上項目一項，青年基金一項; 國家博士后基金特別資助一項，面上項目一項。在Ramanujan，Acta Arith.，DCC，F(xiàn)FA等期刊發(fā)表SCI論文10余篇。
