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A New Criterion on k-Normal Elements over Finite Fields

A New Criterion on k-Normal Elements over Finite Fields

作     者:Aixian ZHANG Keqin FENG Aixian ZHANG;Keqin FENG

作者机构:Department of Mathematical SciencesXi’an University of TechnologyXi’an 710054China Department of Mathematical SciencesTsinghua UniversityBeijing 100084China 

出 版 物:《Chinese Annals of Mathematics,Series B》 (数学年刊(B辑英文版))

年 卷 期:2020年第41卷第5期

页      面:665-678页

核心收录:

学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主  题:Normal basis Finite field Idempotent Linearized polynomial Gauss 

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,*** Thomson,D.(2013),the number of k-normal elements for a fixed finite field extension was calculated and *** this paper the authors present a new criterion on k-normal elements by using idempotents and show some *** criterion was given for usual normal elements before by Zhang et al.(2015).

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