LINEAR COMPLEXITY AND RANDOM SEQUENCES WITH PERIOD 2~n

Let (?)=(S,S,…)be a binary random sequence with period N=2~n,where S=(S_0,…,S_(N-1))is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c(?)=2-(2N+1)2~(-N)-2~(-2N);2)E|c(?)-c(?)|=[2~(c(?)+1)-2]2~(-N)for any sequence (?) with period 2~n;3)N-1+2~(-N)-(n/2+1-2~(-(N-n)))≤E[(?)c(?)]≤N-1+2~(-N)4)2-2~(-(N-1))≤E[(?)|c(?)-c(?)|]≤2-2~(-N)+n/2-2~(-(N-n)),where E and Var stand for taking expectation and variance respectively,c(?) is the linearcomplexity of the sequence (?) and W(b) the Hamming weight of one period of the seqnence (?).     

CORRELATION PROPERTIES OF DE BRUIJN SEQUENCES

Several new bounds for the correlation functions of de Bruijn sequences are derived.It is shown that the set of all primitive de Bruijn sequences have the following two properties:1)for each sequence a in the set with large span n,the magnitude of its auto-correlation funct-ion|r_a(k)|is relatively small compared with the peak 2~n for all k≠0 mod 2~n;2)for each pair of sequences a,b in the set with large span n,the magnitude of their cross-correlation function |r_(ab)(k)| is relatively small compared with the peak 2~n for all k.Some generalizations of the result are also presented.     

LINEAR COMPLEXITY AND THE MINIMAL POLYNOMIAL OF LINEAR RECURRING SEQUENCES OVER Z/(m)

In this note we discuss the annihilating properties of sequences over Z/(m).Byconsidering the linear complexity and the annihilator structure,we derive the uniqueness conditionfor the minimal polynomial,and some related results of decimation sequences.     

BINARY SEQUENCE WITH PERFECT SPREADING STAIRCASE PROFILE OF LINEAR COMPLEXITY

1.IntroductionThelinearcomplexityofasequenceisdefinedasthelengthoftheshortestlinearfeedbackshiftregisterthatcangeneratethesequence.LetS=s182s3''beaninfinitebinarysequence.S(n)=slsZ''sathesubsequenceofSformedbythefirstnbits,L(S(n))=L.thelinearcomplexityo…     

ON THE LINEAR PREDICTABILITY TEST FOR ENCIPHERING SEQUENCES

ＯＮＴＨＥＬＩＮＥＡＲＰＲＥＤＩＣＴＡＢＩＬＩＴＹＴＥＳＴＦＯＲＥＮＣＩＰＨＥＲＩＮＧＳＥＱＵＥＮＣＥＳ￥ＺＥＮＧＫｅｎｃｈｅｎｇ；ＤＡＩＺｏｎｇｄｕｏ（ＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙｏｆｉｎｊｏｒｍａｔｉｏｎＳｅｃｕｒｉｔｙ，Ａｃａｄｅｍｉａ...     

高维动态和大型线性问题的正交试验选优方法

提出了高维动态规划和大型线性规划问题的正交试验选优方法,对于高维动态问题可以使千维动态规划的求解成为可能;对于某些大型线性块角结构问题的求解比单纯形法的运算速度更快．     

POPOV METHOD FOR ROBUST ANALYSIS AND ROBUST SYNTHESIS OF MIMO LINEAR SYSTEMS WITH MRAMETRIC UNCERTAINTIES

ＰＯＰＯＶＭＥＴＨＯＤＦＯＲＲＯＢＵＳＴＡＮＡＬＹＳＩＳＡＮＤＲＯＢＵＳＴＳＹＮＴＨＥＳＩＳＯＦＭＩＭＯＬＩＮＥＡＲＳＹＳＴＥＭＳＷＩＴＨＭＲＡＭＥＴＲＩＣＵＮＣＥＲＴＡＩＮＴＩＥＳ￥ＨＵＡＮＧＹｉ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ...     

STABILITY ROBUSTNESS MEASURES OF LINEAR STATE- SMCE MODELS WITH STRUCTURED PERTURBATIONSCAO Dengqing

1.IntroductionTherobuststabilityanalysisoflinearuncertainsystemshasbeenanactiveresearchtopicincolltroltheoryforsometime.Forexmple,seeDoratoandYedavallil1]andSiljak[']forasummaryofreceatdevelopmelltsinthisarea.Inparticular,thereisconsiderableliteratureavailableonthestabilityrobustnessmeasuresoflinearstate-spacesystemswithparameterperturbationswheretheuncertailltycanbeeithernormbounded(unstructured)orintermsofboundsontheintervals0ftheindividualelemelltsoftheperturbationmatris(structured).Sever…     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.     

CYCLES CONTAINING MANY VERTICES OF SUBSETS IN GRAPHS WITH LARGE DEGREE SUMS AND NEIGHBORHOOD UNIONS

1. ResultsWe use[IJ for terminology and notations not defined here and consider simple graph only.Let G be a graph of order n and X C V(G). A graph G is called 1--tough if w(G\S) 5 ISIfor any S g V(G) with w(G\S) > 1, where w(G\S) denotes the number of components ofgraph G\S. A cycle C of G is called X-longest if no cycle of G contains more venices of Xthan C, and by c(X) we denote the number of venices of X in an X-longest cycle. A cycle Cof G is called X-dominating if all neigh…