A New Criterion on k-Normal Elements over Finite Fields  

作　　者：Aixian ZHANG Keqin FENG 

机构地区：[1]Department of Mathematical Sciences,Xi’an University of Technology,Xi’an 710054,China [2]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China

出　　处：《Chinese Annals of Mathematics,Series B》2020年第5期665-678,共14页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11571107);the Natural Science Basic Research Plan of Shaanxi Province of China(No.2019JQ-333).

摘　　要：The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al.(2013).Several methods to construct k-normal elements were presented by Alizadah et al.(2016)and Huczynska et al.(2013),and the criteria on k-normal elements were given by Alizadah et al.(2016)and Antonio et al.(2018).In the paper by Huczynska,S.,Mullen,G.,Panario,D.and Thomson,D.(2013),the number of k-normal elements for a fixed finite field extension was calculated and estimated.In this paper the authors present a new criterion on k-normal elements by using idempotents and show some examples.Such criterion was given for usual normal elements before by Zhang et al.(2015).

关 键 词：Normal basis Finite field IDEMPOTENT Linearized polynomial GAUSS 

分 类 号：O174.14[理学—数学]