estimation and control of systems with unknown covariance and multiplicative noise the problem of estimation and control for systems with multiplicative noise and unknown second order statistics is considered conditions are found for the existence of a solution based on game theoretic ideas the conditions for the existence of a saddle point for the time invariant filtering problem are necessary and sufficient whereas for all other cases only necessary the central idea of the solution is to convert the stochastic problem to a deterministic optimal control problem whose minimax point is sought with respect to the control filter and unknown statistics parameters the results that are derived show that the problem of estimation for systems with unknown covariances depends on the costate matrix which in turn is a function of the performance measure thus the filter loses one of its best known properties that of independence of the performance functional this property holds not only for the classical kalman filter but also for multiplicative systems

solution bounds of the continuous riccati matrix equation a new approach is proposed for estimating the solution of the continuous algebraic riccati equation care upper and lower solution bounds of the care are presented comparisons show that the present bounds are more general and or tighter than existing results

new upper solution bounds of the continuous algebraic riccati matrix equation by utilizing some linear algebraic techniques new upper bounds of the solution of the continuous algebraic riccati equation care are derived according to the present bounds iterative procedures are also developed for obtaining more precise estimations comparing with existing results the obtained bounds are less restrictive

upper bounds on generalized distances we derive new asymptotic bounds for generalized distances our approach extends the classical hamming plotkin and elias bounds the latter bound involves extending the definition of generalized distances to nonlinear codes

bounds in algebraic riccati and lyapunov equations a survey and some new results this paper summarizes and investigates the relations of a number of bounds for the solutions of the algebraic riccati and lyapunov equations that have been reported during the last two decades also presented are bounds for the unified riccati equation using the delta operator and it is shown that some bounds for the continuous and discrete riccati equations can be unified by them

optimal codes for error detection the probability of undetected error for codes over gf 2 sup m having a generator matrix over gf 2 is studied the optimal codes of dimensions four or less are determined for higher dimensions some properties of optimal codes are determined

bounds on eigenvalues of matrix products with an application to the algebraic riccati equation lower and upper summation bounds for the eigenvalues of the product xy are presented under various restrictions on matrices x y in r sup n n an application to the algebraic riccati equation yields a trace lower bound it is observed that these bounds are tighter than those in the literature

generalized hamming weights of linear codes the generalized hamming weight d sub r c of a binary linear code c is the size of the smallest support of any r dimensional subcode of c the parameter d sub r c determines the code s performance on the wire tap channel of type ii bounds on d sub r c and in some cases exact expressions are derived in particular a generalized griesmer bound for d sub r c is presented and examples are given of codes meeting this bound with equality

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

on the generalized hamming weights of geometric goppa codes we study the generalized hamming weights of geometric goppa codes giving a translation of these weights into arithmetical terms concerning the arithmetic of the curve used to construct the code we derive some results and bounds that we apply to some known codes

parameters of goppa codes revisited we discuss parameters of goppa 1970 codes such as minimum distance covering radius distance distribution and generalized hamming weights by a variation on the exponential sums method and combinatorial arguments we sharpen known bounds on these parameters

robust kalman filtering for discrete time varying uncertain systems with multiplicative noises in this paper a robust finite horizon kalman filter is designed for discrete time varying uncertain systems with both additive and multiplicative noises the system under consideration is subject to both deterministic and stochastic uncertainties sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete riccati difference equations a numerical example is given to show the applicability of the presented method

discriminative feature selection for on line signature verification abstract on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since individuals have different writing habits consistent and discriminative features should be selected to distinguish genuine signatures from forged signatures in this paper two methods which are based on full factorial experiment design and optimal orthogonal experiment design are proposed for selecting discriminative features among candidates to improve the robustness consistency of feature is analyzed at first and more consistent features are selected as candidates for discriminative feature selection to reduce the influences of fluctuations caused by internal and external writing environments changes before verification signatures are effectively aligned to their reference templates based on gaussian mixture model a modified dynamic time warping with signature curve constraint is presented for verification to improve the efficiency comprehensive experiments are implemented based on the data of the open access databases mcyt and svc2004 task2 experimental results verify the effectiveness and robustness of our proposed methods

matrix bounds of the solutions of the continuous and discrete riccati equations a unified approach in this paper a new scheme is introduced to measure the matrix bounds of the continuous and discrete riccati equations by estimating upper and lower matrix bounds of the solution of the unified algebraic riccati equation uare the same measurements for the solutions of the continuous and discrete riccati equations respectively can be obtained in limiting cases according to these obtained matrix bounds several eigenvalue bounds are also defined all the proposed results for the uare are new and more general than previous work some obtained results are compared with those of the literature via numerical examples it is shown that in some cases the presented results are tighter than the existing ones

trace bounds on the covariances of continuous time systems with multiplicative noise matrix equations such as ap pa sup t fpf sup t omega 0 and aq qa sup t qvq fpf sup t omega 0 which arise in the estimation problem of systems with both additive and multiplicative noise are treated trace bounds on the steady state and error covariances p and q are established under complete and incomplete noise information an example illustrates the usefulness of these bounds in determining the size of the estimation error

generalized hamming weights of trace codes linear codes over f sub p often admit a natural representation as trace codes of codes that are defined over an extension field f sub p m in the paper the authors obtain estimates for the weights of subcodes of such trace codes their main result is a far reaching generalization of the carlitz uchiyama bound for the duals of binary bch codes in particular they prove sharp bounds for the generalized hamming weights of a large class of codes including duals of bch codes classical goppa codes melas codes and arbitrary cyclic codes of length n p sup m 1 the main tool is the theory of algebraic functions over finite fields in particular the hasse weil bound for the number of places of degree one

a new approach for upper bound estimations of the solution of the continuous riccati equation by utilizing some linear algebraic techniques a new approach for measuring upper bounds of the solution of the continuous algebraic riccati equation care is developed two upper matrix bounds are developed comparing with those appeared in the literature the obtained bounds are less restrictive or more concise therefore they can be applied easily to deal with control problems

the weight hierarchy of higher dimensional hermitian codes studies a class of projective systems and linear codes corresponding to hermitian varieties over finite fields the weight hierarchy also known as the set of generalized hamming weights of the code is calculated the higher weight distribution is also found

signature alignment based on gmm for on line signature verification on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since writing environments are always changed fluctuations can be caused by signature size location and rotation angle which being various at each inputting signatures should be effectively aligned before verification which can diminish deviations caused by these fluctuations in this study we propose a method of signature alignment based on gaussian mixture model to obtain the best matching in verification a modified dynamic time warping with signature curve constraint is presented to improve the efficiency weight factors are dynamically assigned to features which depend on coefficient of variation to improve the robustness several experiments are implemente d on the open access on line signature databases mcyt and svc2004 task2 the best performances can be provided with equal error rates 2 15 and 2 63 respectively experimental results indicate the effectiveness and robustness of our proposed method signatures are aligned well to reference template based on gaussian mixture model before verification efficiency of verification is improved by modified dynamic time warping with signature curve constraint distance probability is presented to describe the dissimilarity between test signatures and references a strategy of dynamic weight factors being assigned to features depend on coefficient of variation

trace bounds on the solution of the algebraic matrix riccati and lyapunov equation lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix riccati and lyapunov equation are derived the upper trace bound obtained in this note in many cases results in a tighter bound as compared to the upper bound for the maximal eigenvalue proposed in 1 and 2

eigenvalue bounds on the solutions of coupled lyapunov and riccati equations abstract coupled lyapunov and riccati equations of the form p j 0 q a j pa j t gg t q a 0 kc 0 q a 0 kc 0 t j 1 q a j pa j t gg t k m 1 r c m pc m t dd t k t arise in the estimation problem of stochastic systems corrupted by additive and multiplicative noise the matrices p and q are the steady state and estimation error covariances in this paper trace and eigenvalue bounds for p and q are established

using geometric extrema for segment to segment characteristics comparison in online signature verification abstract a signature verification algorithm based on a segment to segment matching is described in which a new approach for finding segment to segment correspondence is proposed in the proposed method geometric extrema are used as segmenting boundaries with two reasons 1 extrema are reproduced with high stability and 2 the properties of extrema are useful in finding segment to segment correspondence in this paper a set of rules for legitimate correspondence between extrema is defined based on their properties which is utilized for the similarity evaluation between segments dynamic programming is then applied to find an optimal correspondence map through experiments the proposed algorithm is assessed to be effective in improving discriminative ability we also showed that the overall performance is further improved by combining the proposed method with the traditional global parametric algorithm

trellis decoding complexity of linear block codes in this partially tutorial paper we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity maximum state and edge dimensions total span length and total vertices edges and mergers we obtain bounds on these complexities as extensions of well known dimension length profile dlp bounds codes meeting these bounds minimize all the complexity measures simultaneously conversely a code attaining the bound for total span length vertices or edges must likewise attain it for all the others we define a notion of uniform optimality that embraces different domains of optimization such as different permutations of a code or different codes with the same parameters and we give examples of uniformly optimal codes and permutations we also give some conditions that identify certain cases when no code or permutation can meet the bounds in addition to dlp based bounds we derive new inequalities relating one complexity measure to another which can be used in conjunction with known bounds on one measure to imply bounds on the others as an application we infer new bounds on maximum state and edge complexity and on total vertices and edges from bounds on span lengths

duality and support weight distributions we show how to compute the support weight distribution a sub i sup r for r spl ges k d sub 2 sup spl perp 3 where d sub 2 sup spl perp is the second minimum support weight of a code provided the weight enumerator of the dual code is known

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

the higher weight enumerators of the doubly even self dual 48 24 12 code an efficient algorithm is presented for calculating higher weight enumerators of linear codes given generator matrices by this algorithm the higher weight enumerators of the unique doubly even self dual code are calculated the algorithm is based on a previously shown relationship between tutte polynomials and higher weight enumerators

duality for poset codes in this paper we extend wei s duality theorem relating the generalized hamming weight hierarchy of a code to the hierarchy of the dual code to the scope of codes with poset metrics as a consequence of this duality theorem we prove some results concerning discrepancy of codes and chain condition for generalized weights

the weight hierarchies of q ary codes of dimension 4 the weight hierarchy of a linear n k q code c over gf q is the sequence d sub 1 d sub 2 d sub k where d sub spl tau is the smallest support of an spl tau dimensional subcode of c the possible weight hierarchies of n 4 q codes are studied in particular the possible weight hierarchies of n 4 3 codes are determined

matrix characterization of linear codes with arbitrary hamming weight hierarchy the support of an n k linear code c over a finite field f q is the set of all coordinate positions such that at least one codeword has a nonzero entry in each of these coordinate position the rth generalized hamming weight d r c 1 leq r leq k of c is defined as the minimum of the cardinalities of the supports of all n r subcodes of c the sequence d 1 c d 2 c d k c is called the hamming weight hierarchy hwh of c the hwh d r c n k r r 1 2 k characterizes maximum distance separable mds codes therefore the matrix characterization of mds codes is also the characterization of codes with the hwh dr c n k r r 1 2 k a linear code c with systematic check matrix i p where i is the n k x n k identity matrix and p is a n k x k matrix is mds iff every square submatrix of p is nonsingular in this paper we extend this characterization to linear codes with arbitrary hwh using this result we characterize near mds codes near near mds n 2 mds codes and a mu mds codes the mds rank of c is the smallest integer n such that d n 1 n k n 1 and the defect vector of c with mds rank n is defined as the ordered set mu1 c mu2 c mu3 c mu n c mu n 1 c where mu i c n k i di c we call c a dually defective code if the defect vector of the code and its dual are the same we also discuss matrix characterization of dually defective codes further the codes meeting the generalized greismer bound are characterized in terms of their generator matrix the hwh of dually defective codes meeting the generalized greismer bound are also reported