the mixed harmonic problem in a bounded cracked domain with dirichlet condition on cracks abstract the mixed dirichlet neumann problem for the laplace equation in a bounded connected plane domain with cuts cracks is studied the neumann condition is given on closed curves making up the boundary of a domain while the dirichlet condition is specified on the cuts the existence of a classical solution is proved by potential theory and boundary integral equation method the integral representation for a solution is obtained in the form of potentials the density in potentials satisfies the uniquely solvable fredholm integral equation of the second kind and index zero singularities of the gradient of the solution at the tips of cuts are investigated

syndrome decoding of reed solomon codes beyond half the minimum distance based on shift register synthesis in this paper a new approach for decoding low rate reed solomon codes beyond half the minimum distance is considered and analyzed the maximum error correcting radius coincides with the error correcting radius of the sudan algorithm published in 1997 however unlike the sudan algorithm the approach described here is not a list decoding algorithm and is not based on polynomial interpolation the algorithm in this paper is rather syndrome based like classical algebraic decoding algorithms the computational complexity of the new algorithm is of the same order as the complexity of the well known berlekamp massey algorithm to decode errors beyond half the minimum distance the new decoder is allowed to fail for some high weight error patterns with a very small probability

simultaneous partial inverses and decoding interleaved reed solomon codes this paper introduces the simultaneous partial inverse problem spi for polynomials and develops its application to decoding interleaved reed solomon codes beyond half the minimum distance while closely related both to standard key equations and to well known pade approximation problems the spi problem stands out in several respects first the spi problem has a unique solution up to a scale factor which satisfies a natural degree bound second the spi problem can be transformed monomialized into an equivalent spi problem where all moduli are monomials third the spi problem can be solved by an efficient algorithm of the berlekamp massey type fourth decoding interleaved reed solomon codes or subfield evaluation codes beyond half the minimum distance can be analyzed in terms of a partial inverse condition for the error pattern if that condition is satisfied then the true error locator polynomial is the unique solution of a standard key equation and can be computed in many different ways including the well known multi sequence berlekamp massey algorithm and the spi algorithm of this paper two of the best performance bounds from the literature the schmidt sidorenko bossert bound and the roth vontobel bound are generalized to hold for the partial inverse condition and thus to apply to several different decoding algorithms

vibrational control of nonlinear systems vibrational stabilizability in this work the theory of vibrational control for nonlinear systems is developed the present paper gives criteria for stabilizability of nonlinear systems by linear multiplicative vibrations by almost periodic forcing and by vector additive vibrations illustrative examples are also considered in a subsequent paper the problem of vibrational controllability and transient behavior will be addressed

non linear dynamics of the follower loaded double pendulum with added support excitation the partially follower loaded elastic double pendulum subjected to excitation of the support parallel to the straight upright pendulum position is studied the effect of small amplitude off resonant high frequency excitation on the linear stability and non linear behaviour of the pendulum is examined by use of the method of direct partition of motion dpm 1 blekhman 1994 vibrational mechanics the model equations are transformed into autonomous equations with the high frequency excitation approximated by equivalent static forces linear stability analysis shows that the support excitation has a stabilizing effect for most system parameters but can also destabilize the upright pendulum position in certain situations local post and pre critical non linear behaviour is analyzed by using centre manifold reduction and normal forms support excitation is seen to change the bifurcational behaviour qualitatively e g supercritical bifurcations may change to become subcritical chaotic behaviour of the pendulum is shown to exist for a wider range of system parameters and initial conditions with added support excitation compared to the case of a fixed support

the neumann problem in a 2 d exterior domain with cuts and singularities at the tips abstract the neumann problem for the harmonic functions in an exterior connected plane region with cuts is studied the problem is considered with different conditions at infinity which lead to different theorems on uniqueness and solvability the existence of a classical solution is proved by potential theory the problem is reduced to a fredholm equation of the second kind which is uniquely solvable explicit formulas for singularities of a gradient of the solution at the tips of the cuts are obtained the results of the paper can be used to model the flow of an ideal fluid over several obstacles including wings

a generalized euclidean algorithm for multisequence shift register synthesis the problem of finding a linear feedback shift register of shortest length capable of generating prescribed multiple sequences is considered a generalized euclidean algorithm which is based on a generalized polynomial division algorithm is presented a necessary and sufficient condition for the uniqueness of the solution is given when the solution is not unique the set of all possible solutions is also derived it is shown that the algorithm can be applied to the decoding of many cyclic codes for which multiple syndrome sequences are available when it is applied to the case of a single sequence the algorithm reduces to that introduced by y sugiyama et al inf control vol 27 p 87 9 feb 1975 in the decoding of bch codes

skew feedback shift register synthesis and decoding interleaved gabidulin codes an efficient algorithm which synthesizes all shortest skew feedback shift registers defined in the paper generating l sequences of varying length over a field is derived and its correctness is proved it generalizes the berlekamp massey algorithm and some other algorithms and has time complexity o ln2 where n is the length of a longest sequence the proposed algorithm can be applied for efficiently solving the key equation when decoding interleaved or direct sum of gabidulin codes beyond half minimum distance those codes have many applications and as shown by kotter and kschischang can be used for random network coding

on the 2 adic complexity and the k error 2 adic complexity of periodic binary sequences a significant difference between the linear complexity and the 2 adic complexity of periodic binary sequences is pointed out in this correspondence based on this observation we present the concept of the symmetric 2 adic complexity of periodic binary sequences the expected value of the 2 adic complexity is determined and a lower bound on the expected value of the symmetric 2 adic complexity of periodic binary sequences is derived we study the variance of the 2 adic complexity of periodic binary sequences and the exact value for it is given because the k adic complexity of periodic binary sequences is unstable we present the concepts of the kappa error 2 adic complexity and the k error symmetric 2 adic complexity and lower bounds on them are also derived in particular we give tighter upper and lower bounds for the minimum k adic complexity of l sequences by substituting two symbols within one period

more on solving systems of power equations it is known that a system of power equations can be reduced to a single variable polynomial equation by exploiting the so called newton s identities in this work we investigate four new types of power equation systems in the first two types we allow the powers to be a mix of positive and negative terms whereas in the literature the system of power equations involves only positive powers the first type involves only positive signs of powers whereas the second type expands to involve both positive and negative signs we present algebraic methods to solve the system and furthermore fully characterize the number of nontrivial solutions the other two types are defined over finite fields and otherwise are the same as the conventional system of power equations the methodology for solving the third type can be viewed as a generalization of the berlekamp algorithm the solution space of the last system is fully characterized despite the fact that the number of equations is two less than the number of unknowns

on the average complexity of reed solomon list decoders the number of monomials required to interpolate a received word in an algebraic list decoder for reed solomon codes depends on the instantaneous channel error and not only on the decoder design parameters the implications of this fact are that the decoder should be able to exhibit lower decoding complexity for low weight errors and consequently enjoy a better average case decoding complexity and a higher decoding throughput on the analytical side this paper studies the dependence of interpolation costs on instantaneous errors in both hard and soft decision decoders on the algorithmic side it provides an efficient interpolation algorithm based on the state of the art interpolation algorithm that enjoys reduced running times for reduced interpolation costs

grobner basis solutions of constrained interpolation problems this paper extends the previous work of the authors on recursive grobner basis techniques in coding theory pade approximation partial realization interpolation and modelling discrete time behaviours we present a general algorithm applicable to a wide range of constrained interpolation problems in coding theory and systems theory including list decoding and m pade approximation

theories and experiments on the stiffening effect of high frequency excitation for continuous elastic systems abstract one effect of strong mechanical high frequency excitation may be to apparently stiffen a structure a well described phenomenon for discrete systems the present study provides theoretical and experimental results on this effect for continuous elastic structures a laboratory experiment is set up for demonstrating and measuring the stiffening effect in a simple setting in the form of a horizontal piano string subjected to longitudinal high frequency excitation at the clamped base and free at the other end a simplest possible theoretical model is set up and analyzed using a hierarchy of three approximating theories each providing valuable insight one of these is capable of predicting the vertical string lift due to stiffening in terms of simple expressions with results that agree very well with experimental measurements for a wide range of conditions it appears that resonance effects cannot be ignored as was done in a few related studies unless the system has very low modal density or heavy damping thus first order consideration to resonance effects is included using the specific example with experimental support to put confidence on the proposed theory expressions for predicting the stiffening effect for a more general class of continuous systems in differential operator form are also provided

an algebraic procedure for decoding beyond e sub bch we present a new way to find all possible error patterns up to a given weight greater than the designed error correcting capability e sub bch possible error positions are localized by indicators our method can be seen as an extension of the step by step decoder introduced by massey 1965 for bch codes we consider the decoding of binary cyclic codes

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

the indian rope trick for a parametrically excited flexible rod linearized analysis it is well known that if a column exceeds a certain critical length it will when placed upright buckle under its own weight in a recent experiment mullin has demonstrated that a column that is l

a new lower bound for the minimum distance of a cyclic code a new lower bound for the minimum distance of a linear code is derived when applied to cyclic codes both the bose chaudhuri hocquenghem bch bound and the hartmann tzeng ht bound are obtained as corollaries examples for which the new bound is superior to these two bounds as well as to the carlitz uchiyama bound are given

some general effects of strong high frequency excitation stiffening biasing and smoothening abstract mechanical high frequency hf excitation provides a working principle behind many industrial and natural applications and phenomena this paper concerns three particular effects of hf excitation that may change the apparent characteristics of mechanical systems 1 stiffening by which the apparent linear stiffness associated with an equilibrium is changed along with derived quantities such as stability and natural frequencies 2 biasing by which the system is biased towards a particular state static or dynamic which does not exist or is unstable in the absence of the hf excitation and 3 smoothening referring to a tendency for discontinuities to be effectively smeared out by hf excitation illustrating first these effects for a few specific systems analytical results are provided that quantify them for a quite general class of mechanical systems this class covers systems that can be modelled by a finite number of second order ordinary differential equations generally non linear with periodically oscillating excitation terms of high frequency and small amplitude the results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems for calculating effects for specific systems using well defined formulas and for possibly designing systems that display prescribed characteristics in the presence of hf excitation

vlsi architectures for soft decision decoding of reed solomon codes soft decision decoding of reed solomon codes delivers significant coding gains over classical minimum distance decoding in this paper we present architectures for polynomial interpolation and factorization the two main steps of the soft decoding algorithm we introduce an algorithmic transformation for reducing the iterations required in generating the interpolation polynomial and present efficient architectures by sharing computations we also describe algorithmic transformations for further reducing the interpolation and factorization latency an area efficient folded pipelined version of the interpolation architecture is also described finally we present an example of a reed solomon soft decoder utilizing the presented architectures having a 250 mbps throughput

a view of gaussian elimination applied to early stopped berklekamp massey algorithm in this paper we adopt a restricted gaussian elimination on the hankel structured augmented syndrome matrix to reinterpret an early stopped version of the berlekamp massey algorithm in which only t e iterations need to be performed for the decoding of bch codes up to t errors where e is the number of errors actually occurring with e leq t instead of the 2t iterations required in the conventional berklekamp massey algorithm the minimality of t e iterations in this early stopped berklekamp massey esbm algorithm is justified and related to the subject of simultaneous error correction and detection in this paper we show that the multiplicative complexity of the esbm algorithm is upper bounded by te e 2 1 forall e leq t and except for a trivial case the esbm algorithm is the most efficient algorithm for finding the error locator polynomial

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

on the minimum distance of cyclic codes the main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds i e bch bound ht bound roos bound this bound is related to a second method for bounding the minimum distance of a cyclic code which we call shifting this method can be even stronger than the first one for all binary cyclic codes of length with two exceptions we show that our methods yield the true minimum distance the two exceptions at the end of our list are a code and its even weight subcode we treat several examples of cyclic codes of length geq 63

sensitivity analysis for problems of dynamic stability abstract in mechanics as well as in physics the most general and important thing is to study the dependence of the characteristics of a physical process on problem parameters problems of dynamic stability for non conservative systems involve determination of eigenvalues and eigenvectors for these problems it is shown in general how the different sensitivity analyses can be performed without any new eigenvalue analyses the main question relates to the change in flutter load as a function of change in stiffness mass boundary conditions or load distribution discretized as well as non discretized examples are presented in details

an algorithm for computing minimal bidirectional linear recurrence relations we consider the problem of computing a linear recurrence relation or equivalently a linear feedback shift register of minimum order for a finite sequence over a field with the additional requirement that not only the highest but also the lowest coefficient of the recurrence is nonzero such a recurrence relation can then be used to generate the sequence in both directions increasing or decreasing order of indices so we call it bidirectional if the field is finite a sequence is periodic if and only if it admits a bidirectional linear recurrence relation for solving the above problem we propose an algorithm similar to the berlekamp massey algorithm and prove its correctness we describe the set of all solutions to this problem and show that if a sequence admits more than one linear recurrence relation then it admits a bidirectional one we also prove some properties regarding the bidirectionality of the recurrences of the prefixes of the sequence

propagation of cracks in elastic media throughout this paper the normal n denotes the interior normal direction i e n f x1 1 p 1 jf x1 j when x approaches from above denoted by and n f x1 1 p 1 jf x1 j from below denoted by in a recent paper 2 the present authors studied the asymptotic behavior of any solution of 1 2 1 4 in a neighborhood of the tip x t taking for simplicity t 0 and assuming that

an algorithm for constructing a minimal partial realization in the multivariable case it is known that the berlekamp massey algorithm from information theory can be used to compute scalar minimal partial realizations recently it has been interpreted in terms of exact modeling of behaviors in this paper we extend these results to the multivariable case we put the behavioral theory of exact modeling to work in deriving an extension of the berlekamp massey algorithm for computing multivariable minimal partial realizations

multisequence shift register synthesis over commutative rings with identity with applications to decoding cyclic codes over integer residue rings we present a new algorithm for solving the multisequence shift register synthesis problem over a commutative ring r with identity given a finite set of r sequences each of length l the complexity of our algorithm in terms of r multiplications is o l sup 2 as l spl rarr spl infin an important application of this algorithm is in the decoding of cyclic codes over z sub q up to the hartmann tzeng bound where q is a prime power characterization of the set of monic characteristic polynomials of a prescribed set of multiple syndrome sequences leads to an efficient decoding procedure which we further extend to decode cyclic codes over z sub m where m is a product of prime powers

stability and chaotic behavior of a pid controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory abstract in this paper we investigate the stability and the onset of chaotic oscillations around the pointing up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions the driven control torque is defined as a proportional plus integral plus derivative pid control of the deviation angle with respect to the pointing down equilibrium position the parameters of the pid controller are tuned by using the routh criterion to obtain a stable weak focus around the pointing up position whose stability is investigated by using the normal form theory the normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model from the harmonic prescribed motions for the pendulum base necessary conditions for chaotic motion are deduced by means of the melnikov function when the pendulum is close to the unstable pointing up position the pid parameters are changed and the chaotic motion is destroyed which is achieved by employing very small control signals even in the presence of random noise the results of the analytical calculations are verified by full numerical simulations

a fast collocation method for acoustic scattering in shallow oceans abstract in this paper we investigate the numerical solution of the integral equation of the second kind reduced by acoustic scattering in shallow oceans with dirichlet condition based on analyzing the singularity of the truncating kernel with a sum of infinite series using our trigonometric interpolatory wavelets and collocation method we obtain the numerical solution which possesses a fast convergence rate like o 2 j moreover the entries of the stiffness matrix can be obtained by fft which lead the computational complexity to decrease obviously

the influence of fast excitation on a continuous system abstract excitation at frequency far beyond dominant resonance frequencies may affect the usual slow dynamics of a mechanical system here an examination of the effects of high frequency excitation on a simple continuous mechanical system a simply supported beam is presented and the possibility of utilizing high frequency excitation to change the system s dynamical properties is considered

extension of the bch decoding algorithm to decode binary cyclic codes up to their maximum error correction capacities the bch algorithm is extended to correct more errors than indicated by the bch bound in the first step of the decoding procedure a number of errors corresponding to a particular case of the hartmann tzeng bound are corrected in the second step full error correction is the goal a measure for the worst case number of field elements of an extension field gf 2 sup m that must be tested for this purpose is given for binary cyclic linear unequal error protection codes as well as for conventional binary cyclic codes

wave diffraction by a half plane with an obstacle perpendicular to the boundary abstract we prove the unique existence of solutions for different types of boundary value problems of wave diffraction by a half plane with a screen or a crack perpendicular to the boundary representations of the solutions are also obtained upon the consideration of some associated operators this is done in a bessel potential spaces framework and for complex non real wave numbers the investigation is mostly based on the construction of explicit operator relations the potential method and a factorization technique for a certain class of oscillating fourier symbols which naturally arise from the problems

image normalization of wiener hopf operators and boundary transmission value problems for a junction of two half planes abstract the present paper deals with an application of the image normalization technique for certain classes of wiener hopf operators whos associated to ill posed boundary transmission value problems we briefly describe the method of normalization and then apply it to boundary transmission value problems issued from diffraction problems for a junction of two half planes which are relevant in mathematical physics applications for each boundary transmission value problem we analyze the conditions under which the associated operator and the equivalent who are not normally solvable and define the corresponding image normalized operators

use of grobner bases to decode binary cyclic codes up to the true minimum distance a general algebraic method for decoding all types of binary cyclic codes is presented it is shown that such a method can correct t d 1 2 errors where d is the true minimum distance of the given cyclic code the key idea behind this decoding technique is a systematic application of the algorithmic procedures of grobner bases to obtain the error locator polynomial l z the discussion begins from a set of syndrome polynomials f and the ideal t f generated by f it is proved here that the process of transforming f to the normalized reduced grobner basis of i f with respect to the purely lexicographical ordering automatically converges to l z furthermore it is shown that l z can be derived from any normalized grobner basis of i f with respect to any admissible total ordering to illustrate this new approach the procedures for decoding certain bch codes and quadratic residue codes are demonstrated

on the decoding of algebraic geometric codes this paper provides a survey of the existing literature on the decoding of algebraic geometric codes definitions theorems and cross references will be given we show what has been done discuss what still has to be done and pose some open problems

the dirichlet neumann harmonic problem in a two dimensional cracked domain with the neumann condition on cracks the mixed dirichlet neumann problem for the laplace equation in a connected plane domain with cuts cracks is studied the dirichlet condition is given on closed curves making up the boundary of a domain while the neumann condition is specified on the cuts the existence of a classical solution is proved by potential theory and the boundary integral equation method the integral representation for a solution is obtained in the form of potentials the density in potentials satisfies the uniquely solvable fredholm integral equation of the second kind and index zero

on the separation of fast and slow motions in mechanical systems with high frequency modulation of the dissipation coefficient abstract dynamics of a model mechanical system with fast and strong oscillations of the damping coefficient has been analyzed by fidlin 2005 6 he has performed the asymptotic analysis of the equation of motion of this system to conclude that these oscillations produce variation in its effective stiffness the present paper continues analysis of dynamics of the system in the regimes of motion treated by fidlin as well as in those left out in his asymptotic solution the results are compared with the results of the solution of the classical mathieu equation which features fast oscillations in the stiffness of a system the influence of stiffness and damping modulations on the stability of motion of corresponding oscillators is studied several engineering applications modeled by the system with oscillations of the damping coefficient are introduced analysis of motion of this system exemplifies how the method of direct separation of motions blekhman 2000 7 can be applied for solving equations with fast oscillating terms depending on the velocities some features of the application of the method of direct separation of motions in this case and in the similar ones are highlighted

studies on the distribution of the shortest linear recurring sequences the distribution of the shortest linear recurrence slr sequences in the z p field and over the z p e ring is studied it is found that the length of the shortest linear recurrent slrl is always equal to n 2 if n is even and n 2 1 if n is odd in the z p field respectively on the other hand over the z p e ring the number of sequences with length n can also be calculated the recurring distribution regulation of the shortest linear recurring sequences is also found to solve the problem of calculating the slrl a new simple representation of the berlekamp massey algorithm is developed as well

effective properties of mechanical systems under high frequency excitation at multiple frequencies effects of strong high frequency excitation at multiple frequencies multi hfe are analyzed for a class of generally nonlinear systems the effects are illustrated for a simple pendulum system with a vibrating support and for a parametrically excited flexible beam for the latter theoretical predictions are supported by experimental observations providing good agreement for a wide range of excitation conditions the main effect of strong multi hfe is to change the effective or apparent stiffness in a manner similar to that of mono hfe provided the hfe frequencies are well separated and non resonant then the change in effective stiffness is proportional to the sum of squared excitation velocities and the corresponding changes in equilibria equilibrium stability and natural frequencies can be computed as for the mono hfe case when there are two or more close excitation frequencies an additional contribution of slowly oscillating stiffness appears this may cause strong parametric resonance at conditions that might not appear obvious i e when the difference in two hfe frequencies is near twice an effective system natural frequency which due to the hfe itself is shifted away from the natural frequency without hfe also it is shown that strong multi hfe can stabilize otherwise unstable equilibria but generally this requires the frequencies to be well separated thus continuous broadband and random hfe does not have a uniquely stabilizing effect paralleling that of mono hfe or multi hfe with non close frequencies the general results may be used to investigate or utilize general effects or as a shortcut to calculate effective properties for specific systems or to calculate averaged equations of motion that may be much faster to simulate numerically

the modified jump problem for the laplace equation and singularities at the tips the boundary value problem for the laplace equation outside several cuts in a plane is studied the jump of the solution of the laplace equation and the boundary condition containing the jump of its normal derivative are specified of the cuts the unique solution of this problem is obtained the problem is reduced to the uniquely solvable fredholm equation of the second kind and index zero the singularities at the ends of the cuts are investigated

the mixed harmonic problem in an exterior cracked domain with dirichlet condition on cracks the mixed dirichlet neumann problem for the laplace equation in an unboundedconnected plane domain with cuts cracks is studied the neumann condition is given on closed curves making up the boundary of the domain while the dirichlet condition is specified on the cuts the existence of a classical solution is proved by means of potential theory and the boundary integral equation method the integral representation for a solution is obtained in the form of potentials the density in potentials satisfies the uniquely solvable fredholm integral equation of the second kind and index zero singularities of the gradient of the solution at the tips of cuts are investigated

the impedance problem for the propagative helmholtz equation in interior multiply connected domain abstract the impedance problem for the propagative helmholtz equation in the interior multiply connected domain is studied in two and three dimensions by a special modification of a boundary integral equation method additional boundaries are introduced inside interior parts of the boundary of the domain the solution of the problem is obtained in the form of a single layer potential on the whole boundary the density in the potential satisfies the uniquely solvable fredholm equation of the second kind and can be computed by standard codes in fact our method holds for any positive wave numbers

on constructing a shortest linear recurrence relation it has been shown in the literature that a formulation of the minimal partial realization problem in terms of exact modeling of a behavior lends itself to an iterative polynomial solution for the scalar case we explicitly present such a solution in full detail unlike classical solution methods based on hankel matrices the algorithm is constructive it iteratively constructs a partial realization of minimal mcmillian degree the algorithm is known in information theory as the berlekamp massey algorithm and is used for constructing a shortest linear recurrence relation for a finite sequence of numbers

simplified understanding and efficient decoding of a class of algebraic geometric codes an efficient decoding algorithm for algebraic geometric codes is presented for codes from a large class of irreducible plane curves including hermitian curves it can correct up to d 1 2 errors where d is the designed minimum distance with it we also obtain a proof of d sub min spl ges d without directly using the riemann roch theorem the algorithm consists of gaussian elimination on a specially arranged syndrome matrix followed by a novel majority voting scheme a fast implementation incorporating block hankel matrix techniques is obtained whose worst case running time is o mn sup 2 where m is the degree of the curve applications of our techniques to decoding other algebraic geometric codes to decoding bch codes to actual minimum distance and to two dimensional shift register synthesis are also presented

generalized solvability and optimization of a parabolic system with a discontinuous solution abstract we consider the following linear parabolic system in a domain with a thin low permeable insertion imperfect interface u t q u f t k u t q 1 q 2 r n u t 0 0 u 0 k k i j i j 1 n n r n 0 u lim 0 n r n 0 t 0 q 3 q 1 q 2 we consider a new formulation of the problem where the unknowns are u and the parabolic problem is converted to a first order system of partial differential equations with distributional coefficients we also prove inequalities for negative norms for the parabolic operator with the distributional coefficients and theorems of existence and uniqueness for optimization problems for the processes we show existence of optimal controls investigate smoothness of a performance criterion and give a simple condition for controllability of the system in addition we consider applications of the obtained results to a pulse control problem and prove convergence of a control mapping regularization procedure

minimal polynomial algorithms for finite sequences in this paper we show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of an algorithm in a recent paper of a salagean

linearized shift register synthesis an efficient algorithm synthesizing all shortest q linearized feedback shift registers generating a given sequence of length n over a finite field bbfqm is derived and its correctness is proved this algorithm which is a generalization of the berlekamp massey algorithm has time complexity o ln o n2 operations in bbfqm where l is the linearized complexity of the sequence the algorithm can be applied for efficiently solving the key equation when decoding gabidulin codes