周期为p~(n+1)的GF(q)上广义分圆序列的线性复杂度

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英文篇名：The linear complexity of p~(n+1)-periodic generalized cyclotomic sequence over GF(q) 作者：胡传方 ; 岳勤 英文作者：HU Chuanfang,YUE Qin(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China) 关键词：广义分圆序列 ; 线性复杂度 ; 本原单位根 英文关键词：generalized cyclotomic sequence;linear complexity;primitive root of unity 中文刊名：NJLY 英文刊名：Journal of Nanjing Forestry University(Natural Sciences Edition) 机构：南京航空航天大学理学院; 出版日期：2012-09-15 出版单位：南京林业大学学报(自然科学版) 年：2012 期：v.36;No.161 基金：国家自然科学基金项目(10971250,11171150) 语种：中文; 页：NJLY201205029 页数：3 CN：05 ISSN：32-1161/S 分类号：148-150

摘要

主要研究周期为pn+1的q元域上广义分圆序列的线性复杂度,即把二元域上Edemskii的研究结果推广到一般GF(q)上。这里利用分圆数和部分指数和来给出具体的关于线性复杂度的计算公式。
        This paper mainly researched the linear complexity of pn+1-periodic generalized cyclotomic sequences,which generalize Edemskii's results which is mentioned in the first reference from binary field to GF(q).In this paper,cyclotomic number and sums of partial index number will be used to give concrete computation equation of the linear complexity.

引文

[1]冯克勤,刘凤梅.代数与通信[M].北京:高等教育出版社,2005.
    [2]Lidl R,Niederreiter H.Finite fields:encyclopedia of mathematicsand its applications[C]//Computers and Mathematics with Appli-cations.New York:Elsevier Science Publishing Company,1997.
    [3]Ding C.Complexity of generalized cyclo-tomic binary sequence of or-der 2[J].Finite Fields and Their Applications,1997(3):159-174.
    [4]Edemskii V A.On the linear complexity of binary sequences onthe basis of biquadratic and sextic residue classes[J].DiscreteMath Appl,2010,20(1):75-84.
    [5]Edemskii V A.About computation of the linear complexity ofgeneralized cyclotomic sequences with period pn+1,to appear Des[J].Springer:Codes Cryptography,2011,61(3):251-260.
    [6]Dickson L E.Cyclotomy,higher congruences,and Waring'sproblem[J].Amer J Math,1935,57:391-424,463-473.
    [7]Hall M.Combinatorial Theory[M].2nd Edition.New York:Wl-ley,1975.
    [8]胡丽琴.高斯周期、分圆序列及码本[D].南京:南京航空航天大学,2012.
    [9]Irland K,Rosen M.A Classical Introduction to Modern NumberTheory[M].2nd Edition.Berlin:Springer-Verlag,2003.