a lower bound on the undetected error probability and strictly optimal codes error detection is a simple technique used in various communication and memory systems to enhance reliability we study the probability that a q ary linear or nonlinear block code of length n and size m fails to detect an error a lower bound on this undetected error probability is derived in terms of q n and m the new bound improves upon other bounds mentioned in the literature even those that hold only for linear codes block codes whose undetected error probability equals the new lower bound are investigated we call these codes strictly optimal codes and give a combinatorial characterization of them we also present necessary and sufficient conditions for their existence in particular we find all values of n and m for which strictly optimal binary codes exist and determine the structure of all of them for example we construct strictly optimal binary coded decimal codes of length four and five and we show that these are the only possible lengths of such codes

on the traveling salesman problem in binary hamming spaces given a subset x of vertices of the n cube i e the n dimensional hamming space we are interested in the solution of the traveling salesman problem namely the minimal length of a cycle passing through all vertices of x for a given number m we estimate the maximum of these lengths when x ranges over all possible choices of sets of m vertices asymptotically our estimates show that for a number m of vertices growing exponentially in n the maximum is attained for a code with maximal possible minimum distance

tradeoff based decomposition and decision making in multiobjective programming to facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision making a multiobjective decomposition scheme is proposed that restructures the original problem as a collection of smaller sized subproblems with only subsets of the original criteria a priori preferences on objective tradeoffs are integrated into this process by modifying the ordinary pareto order by more general domination cones and decision makers are supported by an interactive decision making procedure to coordinate any remaining tradeoffs using concepts of approximate efficiency a theoretical foundation for this method is provided and an illustrative application to multiobjective portfolio optimization is described in detail

on the undetected error probability of triple error correcting bch codes the probability of undetected error p sub u epsilon for the primitive triple error correcting bch codes of blocklength 2 sup m 1 used solely for error detection on a binary symmetric channel with crossover probability epsilon

k means inverse regression li suggested the method of sliced inverse regression for dimension reduction in regressions with a univariate response in this article we extend that method to multivariate regressions by introducing a new way of performing the slicing this method applies for any number of response variables and may be particularly useful at the outset of an analysis before positing a multivariate model the emphasis is on application no new asymptotic theory is presented

a reference direction approach to multiple objective integer linear programming abstract we propose the use of a reference direction reference point approach to solving multiple objective integer linear programming problems the reference direction reference point is determined by the aspiration levels for the criteria that the decision maker wants to improve within this framework two methods are developed viz a pure integer method that operates entirely with integer solutions and a continuous integer method that works with continuous solutions and finds an integer solution closest to the continuous solution in terms of the achievement scalarizing function obviously the pure integer method is time consuming we therefore propose a decision support system that combines the two methods this way the adbantages of each method can be used to their fullest extent we illustrate the proposed decision support system with a numerical example

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

multiobjective solution of the uncapacitated plant location problem abstract in this paper we consider the discrete multiobjective uncapacitated plant location problem we present an exact and an approximate approach to obtain the set of non dominated solutions the two approaches resort to dynamic programming to generate in an efficient way the non dominated solution sets the solution methods that solve the problems associated with the generated states are based on the decomposition of the problem on two nested subproblems we define lower and upper bound sets that lead to elimination tests that have shown to have a high performance computational experiments on a set of test problems show the good performance of the proposal

an interactive reference point approach for multiobjective mixed integer programming using branch and bound abstract we propose an interactive reference point approach for multiple objective mixed integer linear programming problems that exploits the use of branch and bound techniques for solving the scalarizing programs at each dialogue phase the decision maker must specify a criterion reference point or just choose an objective function he she wants to improve in respect to the previous efficient nondominated solution in the latter case a directional search is performed adjusting automatically the reference point used at each stage tchebycheff mixed integer scalarizing programs are successively solved by branch and bound postoptimality techniques have been developed enabling the algorithm to profit from previous computations to solve the next scalarizing programs the previous branch and bound tree is used as a starting point and operations of simplification and branching are then performed to obtain a new efficient solution computational results have shown that this approach is effective for carrying out directional or local searches for efficient solutions

preference structure representation using convex cones in multicriteria integer programming a new efficient system of representing the decision maker s preference structure in solving multicriteria integer programming problems is developed the problem is solved by an interactive branch and bound method that employs the procedure of zionts and wallenius zionts s j wallenius 1983 an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions management sci 295 for multicriteria linear programming the decision maker s underlying utility function is assumed to be pseudoconcave and his pairwise comparisons of decision alternatives are used to determine his preference structure in terms of certain convex cones in the objective function space and constraints on the weights on the objectives in the weight space the two forms of preference structure representation are interrelated and their underlying theory is developed the primary objective of a representation scheme is exactness and in this respect it is shown that the constraints on the weights are not adequate for representing nonlinear utility functions on the other hand the convex cones exactly represent any quasiconcave utility function and clearly avoid the approximations and inaccuracies in other utility assessment systems accordingly an efficient ordered representation using convex cones is developed an algorithmic framework for multicriteria integer programming that integrates the representation using convex cones with the branch and bound solution procedure is developed computational experience with bicriteria problems having up to 80 variables and 40 constraints is presented

new upper bounds on error exponents we derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels this is an improvement on the best earlier known bounds by shannon gallager berlekamp 1967 and mceliece omura 1977 for the probability of undetected error the new bounds are better than the bounds by levenshtein 1978 1989 and the bound by abdel ghaffar see ibid vol 43 p 1489 502 1997 moreover we further extend the range of rates where the undetected error exponent is known to be exact the new bounds are based on an analysis of possible distance distributions of the codes along with some inequalities relating the distance distributions to the error probabilities

on the undetected error probability of nonlinear binary constant weight codes the undetected error probability uep of binary n 2 spl delta m nonlinear constant weight codes over the binary symmetric channel bsc is investigated where n is the blocklength m is the weight of codeword and 2 spl delta is the minimum distance of the codes the distance distribution of the n 2 m nonlinear constant weight codes is evaluated it is proven in this paper that the 5 2 2 code 5 2 3 code 6 2 3 code 7 2 4 code 7 2 3 code and 8 2 4 code are the only proper error detecting codes in the n 2 m nonlinear constant weight codes for n spl ges 5 in the sense that their uep is increased monotonically with the channel error rate p of course all these proper codes are m out of n codes furthermore it is conjectured that except for the cases of n spl les 4 spl delta there are no proper error detecting binary n 2 spl delta m nonlinear constant weight codes for n 8 and spl deltaspl ges 1

sufficient conditions for good and proper error detecting codes the performance of linear block codes over a finite field is investigated when they are used for pure error detection sufficient conditions for a code to be good or proper for error detection are derived

poor error correction codes are poor error detection codes corresp we show that binary group codes that do not satisfy the asymptotic varshamov gilbert bound have an undesirable characteristic when used as error detection codes for transmission over the binary symmetric channel

the duals of mmd codes are proper for error detection a linear code when used for error detection on a symmetric channel is said to be proper if the corresponding undetected error probability increases monotonically in spl epsiv the symbol error probability of the channel such codes are generally considered to perform well in error detection a number of well known classes of linear codes are proper e g the perfect codes mds codes macdonald s codes mmd codes and some near mds codes the aim of this work is to show that also the duals of mmd codes are proper

evaluation of the undetected error probability of single parity check product codes in this paper an expression for the undetected error probability p epsilon of single parity check product spcp codes used for error detection over a binary symmetric channel is derived it is shown that square spcp codes need not obey a certain commonly used bound approximate expressions for the maximum p epsilon and the corresponding maximizing e are given

an upper bound on the ratio of the probabilities of subgroups and cosets corresp through a counterexample redinbo s upper bound on the ratio of the probability of a group and that of its coset is shown to be incorrect the given example is also shown to provide a new upper bound

the average value for the probability of an undetected error a new identity for the weight enumerator of a code is derived the new identity is shown to be related to the average value of the probability of an undetected error when is a continuous random variable

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

an interactive procedure for multiple objective integer linear programming problems abstract there are many practical problems where the objective functions and the constraints can be represented by linear functions but the decision variables are restricted to only integer values our objective is to present an interactive procedure for the multiple objective integer linear programming problem that is fast does not place too many demands on the decision maker and can be implemented without requiring any special software we illustrate the proposed procedure with a numerical example and report some computational experience

the probability of undetected error for binary constant weight codes in this correspondence we study the probability of undetected error for binary constant weight codes first we derive a new formula on the probability of undetected error for binary constant weight codes second using this new formula and linear programming we give two new lower bounds on the probability of undetected error for binary constant weight codes these two new lower bounds improve on previously known lower bounds in certain cases furthermore we show that these two lower bounds are tight if and only if the binary constant weight codes are generated from certain t designs in combinatorial design theory this means that these binary constant weight codes generated from certain t designs are uniformly optimal for error detection along the way we determine the distance distributions of such binary constant weight codes finally several examples are given to illustrate the results obtained in this correspondence

the mmd codes are proper for error detection the undetected error probability of a linear code used to detect errors on a symmetric channel is a function of the symbol error probability spl epsi of the channel and involves the weight distribution of the code the code is proper if the undetected error probability increases monotonously in spl epsi proper codes are generally considered to perform well in error detection we show in this correspondence that maximum minimum distance mmd codes are proper

an algorithm for the multiple objective integer linear programming problem abstract a technique is presented for solving the multiple objective integer linear programming problem the technique can be used to identify some or all efficient solutions while the technique is applicable with any integer programming algorithm it is well suited for implementation using integer postoptimality techniques such an implementation based on balas additive algorithm is described for problems with zero one variables

on the undetected error probability of binary expansions of reed solomon codes it has been shown by kasami and lin see ieee trans commun vol 32 p 998 1984 that n k reed solomon codes used over a q ary symmetric channel are proper in this correspondence it is shown that the binary expansions of these codes and their extensions when used on the binary symmetric channel are not necessarily proper in particular certain codes of rate less than 1 log sub 2 m m 1 m log sub 2 m 1 where m log sub 2 q are not proper

on the probability of undetected error for linear block codes the problem of computing the probability of undetected error is considered for linear block codes used for error detection the recent literature is first reviewed and several results are extended it is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual using the dual code formulation the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes several bounds on the undetected error probability are then presented we conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained an efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

cut a multicriteria approach for concavifiable preferences we consider the problem of helping a decision maker dm choose from a set of multiattributed objects when her preferences are concavifiable i e representable by a concave value function we establish conditions under which preferences or preference intensities are concavifiable we also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the dm this can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure we report on the practical use of this procedure with several dms for a flat choice problem and its computational performance on a set of project portfolio selection problem instances the use of preference intensities is found to provide significant improvements to the performance of the procedure

performance of rs coded m ary modulation with and without symbol overlapping in this paper we present analytical bit error probability results for m ary modulation concatenated with reed solomon rs codes the analysis of bit error probability is nontrivial as the number of bits per symbol for the rs codes may not be an integer multiple of the number of bits per symbol for a modulation symbol we propose a markov chain technique which allows analytical evaluation of the bit error probability for such cases the performance of rs coding with coherent biorthogonal coherent non coherent orthogonal modulation over an additive white gaussian noise awgn channel is evaluated simulation of the bit error probability of rs code concatenated with a nordstrom robinson nr code as an inner code is performed and compared with the case of biorthogonal modulation from the results we notice that a stronger inner code gives better bit error probability in addition the throughput of the coded system with biorthogonal modulation over an awgn channel is discussed for a rayleigh flat fading and block fading channel we analyze the bit error probability of rs codes concatenated with biorthogonal modulation from the result we notice that a stronger outer code gives a better bit error probability for the case of rayleigh flat fading channel

malfunction in the peterson gorenstein zierler decoder most versions of the peterson gorenstein zierler pgz decoding algorithm are not true bounded distance decoding algorithms in the sense that when a received vector is not in the decoding sphere of any codeword the algorithm does not always declare a decoding failure for a t error correcting bch code if the received vector is at distance i i spl les t from a codeword in a supercode with bch distance t i 1 the decoder will output that codeword from the supercede if that codeword is not a member of the t error correcting code then decoder malfunction is said to have occurred we describe the necessary and sufficient conditions for decoder malfunction and show that malfunction can be avoided in the pgz decoder by checking t spl nu equations where spl nu is the number of errors hypothesized by the decoder a formula for the probability of decoder malfunction is also given and the significance of decoder malfunction is considered for pgz decoders and high speed berlekamp massey decoders

interactive multidimensional programming models for locational decisions abstract the paper is devoted to an extension of traditional location theory in two directions first the usual assumption of a single cost function will be abandoned by introducing multiple objectives this gives rise to a multidimensional programming framework for the traditional location models the paper provides a solution algorithm for the latter problem next the assumption of a uniform space will be tackled by taking account of discrete candidate locations this problem can be solved by means of an adjusted multiciteria analysis the solution algorithms for both extensions are based on an interactive strategy so that the decision maker may identify the most favourable location in a finite number of steps

a branch and bound algorithm for mixed zero one multiple objective linear programming abstract in this paper a branch and bound algorithm for the generation of the efficient set in mixed zero one multiple objective linear programming problems is presented the algorithm is developed as to take account of the multiple objectives in the node fathoming procedure in order to extend the algorithm s applicability to large sized problems from real life an interactive procedure is introduced which systematically reduces the number of efficient points and thus saves considerable computational effort without losing essential information the algorithm is tested in randomly generated problems along with a case study conceming the power generation sector

necessary conditions for good error detection the problem of determining the error detection capabilities of linear codes where the channel is a binary symmetric channel is addressed necessary conditions are given on the number of codewords in an n k linear code and its dual for the probability of an undetected error to be upper bounded by 2 sup n k

solving the biobjective zero one knapsack problem by an efficient lp based heuristic abstract in this paper we propose a simple and useful method the core of which is an efficient lp based heuristic for solving biobjective 0 1 knapsack problems extensive computational experiments show that the proposed method is able to generate a good approximation to the nondominated set very efficiently we also suggest three qualitative criteria to evaluate such an approximation in addition the method can be extended to other problems having properties similar to the knapsack problem

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

preference convex unanimity in multiple criteria decision making the approach which results in the definition of stochastic dominance orders for risky decision making can also be applied to the nonrisky case that is one may postulate that alternative x dominates alternative y if x is preferred to y by every possible decision maker with specified preference characteristics one such unanimity order is the standard componentwise vector order of multiple objective optimization in this paper a unanimity order is constructed based upon characteristics of preference convexity in conjunction with finitely many elicited preference responses since the new order properly includes the vector order the corresponding efficient frontier may be smaller

binary linear quasi perfect codes are normal whether quasi perfect codes are normal is addressed let c be a code of length n dimension k covering radius r and minimal distance d it is proved that c is normal if d or 2r 1 hence all quasi perfect codes are normal consequently any n k r binary linear code with minimal distance d or 2r 1 is normal

asymptotically optimal cells for a historgram on examine les proprietes de l histogramme lorsque les cellules sont arbitraires on obtient une expression asymptotique pour l infimum de l erreur quadratique moyenne integree mise sur toutes les partitions

on the monotonic property of the probability of undetected error for a shortened code the monotonic property of the probability of undetected error is considered when a shortened code of a linear code over gf q is used for error detection on a q ary symmetric channel some conditions are presented under which the probability of undetected error is or is not monotonic with respect to the code length or the symbol error probability it is shown that the probability of undetected error for a maximum distance separable code is monotonic with respect to the codelength it is also shown that the probability of undetected error of a shortened code of any binary cyclic hamming code generated by a trinomial is not monotonic with respect to the bit error rate if the code length is short

approximations for the probability in the tails of the binomial distribution corresp upper and lower bounds for the probability in the tails of a binomial distribution are investigated new bounds are obtained which are computationally simple and in the case of the lower bound significantly better than previously known bounds

performance of reed solomon coded frequency hop spread spectrum communications in partial band interference this paper is concerned with the performance of a communications system which utilizes frequency hop spread spectrum diversity transmission reed solomon coding and parallel error correction and erasure correction decoding both binary signaling and m ary orthogonal signaling are considered the goals are twofold first it is desirable to provide good performance in partial band gaussian noise interference by use of coding and diversity with an efficient error correction algorithm second it is necessary to totally neutralize narrow band interference regardless of the power level or statistical distribution of the interference in order to have an effective spread spectrum system through an analysis of the effects of partial band interference on a frequency hop spread spectrum system with diversity it is shown that the use of reedsolomon coding with a parallel errors and erasures decoding algorithm accomplishes these goals the paper also investigates the accuracy of the chernoff bound as an approximation to the true performance of a frequency hop spreadspectrum communication system with diversity side information m ary orthogonal signaling and reed solomon coding the performance results presented in the paper are based on analysis and computer evaluation approximate results based on the chernoff bound are also given it is shown that the chernoff bound for m ary orthogonal signaling gives a very poor approximation for many cases of interest this is largely due to the looseness of the union bound

direct variance design a multiobjective control theory a theory for designing linear state feedback controllers to directly accommodate variance constraints imposed on the system states is offered such controllers guarantee an average closed loop response to gaussian input disturbances the method provides a mechanism for directly assigning all variance values the diagonal elements of the covariance matrix to the closed loop system the theory may be viewed as offering direct access to a new set of design variables the state variances

the weight distribution of cosets sullivan s 1967 inequality between the weight distribution function of a binary linear code and the weight distribution function of a proper subset of the code is generalized to linear codes over arbitrary finite fields

on the computation of the performance probabilities for block codes with a bounded distance decoding rule when a block code is used on a discrete memoryless channel with an incomplete decoding rule that is based on a generalized distance the probability of decoding failure the probability of erroneous decoding and the expected number of symbol decoding errors can be expressed in terms of the generalized weight enumerator polynomials of the code for the symmetric erasure channel numerically stable methods to compute these probabilities or expectations are proposed for binary codes whose distance distributions are known and for linear maximum distance separable mds codes the method for linear mds codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution numerical examples include a triple error correcting bose chaudhuri hocquenghem bch code of length 63 and a reed solomon code of length 1023 and minimum distance 31

multicriteria integer programming a hybrid dynamic programming recursive approach dynamic programming recursive equations are used to develop a procedure to obtain the set of efficient solutions to the multicriteria integer linear programming problem an alternate method is produced by combining this procedure with branch and bound rules computational results are reported

on the histogram as a density estimator l 2 theory let f be a probability density on an interval i finite or infinite i includes its finite endpoints if any and f vanishes outside of i let x1 x k be independent random variables with common density f the empirical histogram for the x s is often used to estimate f to define this object choose a reference point xosi and a cell width h let nj be the number of x s falling in the j th class interval

an interactive dynamic programming approach to multicriteria discrete programming abstract several interactive schemes for solving multicriteria discrete programming problems are developed under a dynamic programming framework it is assumed that the decision maker s preference structure satisfies the conditions of transitivity monotonicity and nonsatiation hybrid procedures are also structured by including branch and bound ideas into the recursions initial computational results are offered

on the performance of the ternary 13 7 5 quadratic residue code we investigate the weight structure and error correcting performance of the ternary 13 7 5 quadratic residue code it is shown that the covering radius of the code is equal to three and it is t proper for error correction for any t 0 1 2 two decoding algorithms are suggested

interactive relaxation method for a broad class of integer and continuous nonlinear multiple criteria problems an interactive decomposition algorithm for solving a broad class of multiple criteria mc problems is presented in this paper on the one hand the method is designed to solve a broad class of mc problems including complex ones i e problems with nonlinear objective functions and nonlinear constraints with continuous and or integer valued decision variables and with an unknown underlying nonlinear preference function on the other hand the method is intended to reduce the assessment burden on the decision maker dm by simplifying and facilitating the task of making preference assessments and tradeoffs the method is efficient from a computational standpoint since the only program that needs to be solved at each iteration is linear in the decision variables also the algorithm is capable of producing lower and upper bounds lb and ub on the optimal objective value of the mc problem at each iteration although the dm s preference function is not assumed to be known explicitly lb and ub can be used to terminate the search prematurely at a satisfactory good enough solution and consequently to reduce the computational time as well as the number of preference assessments that the dm must make finally all the tradeoffs that the dm is required to make are of the form of ordinal paired comparisons most of which are particularly simple since they involve changes in only two criteria at a time also all the preference assessments are made in the context of feasible solutions only

error detection with a class of irreducible binary cyclic codes and their dual codes the irreducible binary cyclic codes of even dimension introduced by delsarte and goethals in 1970 constitute a parametric class with three parameters we show that these codes and their duals are either proper or not good for error detection

an interactive algorithm for solving multiple objective integer linear programming problems abstract we propose a reference direction based interactive algorithm to solve multiple objective integer linear programming moilp problems at each iteration of the solution procedure the algorithm finds weak nondominated solutions to the relaxed moilp problem only at certain iterations if the dm so desires an additional mixed integer programming problem is solved to find an integer weak nondominated solution which is close to the current continuous weak nondominated solution to the relaxed moilp problem in the proposed algorithm dm has to provide only the reference point at each iteration no special software is required to implement the proposed algorithm the algorithm is illustrated with an example

generalizations of the korzhik bound corresp the probability of undetected error is studied when a code is used both for error correction and error detection a number of generalizations is given of an upper bound of korzhik on the minimal probability of undetected error for an n k code

a review of interactive methods for multiobjective integer and mixed integer programming this paper makes a review of interactive methods devoted to multiobjective integer and mixed integer programming moip momip problems the basic concepts concerning the characterization of the non dominated solution set are first introduced followed by a remark about non interactive methods vs interactive methods then we focus on interactive moip momip methods including their characterization according to the type of preference information required from the decision maker the computing process used to determine non dominated solutions and the interactive protocol used to communicate with the decision maker we try to draw out some contrasts and similarities of the different types of methods

generalized dynamic programming for multicriteria optimization abstract applications of dynamic programming dp to multicriteria sequential decision problems involving the optimization of a multicriteria preference function have been rare this is due to the ease with which dp s monotonicity assumption can be violated in such situations generalized dp avoids the potential pitfalls created by this absence of monotonicity thereby guaranteeing optimality the methodology is applied to a prototypical multicriteria dp problem namely a multicriteria version of the shortest path problem

binary constant weight codes for error detection the undetected error probability of binary constant weight codes on a binary symmetric channel is studied in this correspondence first we present a necessary condition for the binary constant weight codes to be proper for error detection then by using the necessary condition we study the error detection capability of binary optimum constant weight codes

on the probability of undetected error for the maximum distance separable codes in this paper we investigate the performance of maximum distance separable codes with symbols from gf q when they are used for pure error detection or for simultaneous error correction and detection over a q input and q output discret memoryless channel with symbol error probability e first we show that the probability of undetected error for an mds code used for pure error detection is upper bounded by q r and decreases monotonically as edecreases from q 1 q to 0 where r is the number of parity check symbols of the code then we show that the probability of undetected error for an mds code used for correcting t or fewer symbol errors is upper bounded by q r sum min i 0 max t min i max n q 1 i and decreases monotonically as e decreases from q 1 q to 0 these results show that the mds codes are effective for both pure error detection and simultaneous error correction and detection

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

undetected error probabilities of binary primitive bch codes for both error correction and detection we investigate the undetected error probabilities for bounded distance decoding of binary primitive bch codes when they are used for both error correction and detection on a binary symmetric channel we show that the undetected error probability of binary linear codes can be simplified and quantified if the weight distribution of the code is binomial like we obtain bounds on the undetected error probability of binary primitive bch codes by applying the result to the code and show that the bounds are quantified by the deviation factor of the true weight distribution from the binomial like weight distribution

using codes for error correction and detection corresp a linear code c over gf q is good for t error correction and error detection if p c t epsilon leq p c t q 1 q for all epsilon 0 leq epsilon leq q 1 q where p c t epsilon is the probability of an undetected error after a codeword in c is transmitted over a q ary symmetric channel with error probability epsilon and correction is performed for all error patterns with t or fewer errors a sufficient condition for a code to be good is derived this sufficient condition is easy to check and examples to illustrate the method are given

theory and applications of generalized dynamic programming an overview abstract extensions of dynamic programming dp into generalized preference structures such as exist in multicriteria optimization have invariably assumed sufficient structure to ensure the validity of bellman s principle of optimality or the presence of monotonicity hence ensuring the validity of the functional equations of dp often however the only reasonable formulation of problem in terms of the size of the resulting state space is one for which neither monotonicity nor the strong principle of optimality is satisfied generalized dp based on a weaker principle of optimality is a generalization of dp that produces optimal solutions even in the absence of monotonicity it is shown both to subsume conventional dp and to provide an alternative means of implementing mitten s preference order dp this paper provides an overview of generalized dp and its applications to date summarizing our computational experiences in the process

a lower bound on the probability of undetected error for binary constant weight codes in this correspondence we study the probability of undetected error for binary constant weight codes first we derive a new lower bound on the probability of undetected error for binary constant weight codes next we show that this bound is tight if and only if the binary constant weight codes are generated from certain t designs in combinatorial design theory this means that these binary constant weight codes generated from certain t designs are uniformly optimal for error detection along the way we determine the distance distributions of such binary constant weight codes in particular it is shown that binary constant weight codes generated from steiner systems are uniformly optimal for error detection thus we prove a conjecture of xia fu jiang and ling furthermore the distance distribution of a binary constant weight code generated from a steiner system is determined finally we study the exponent of the probability of undetected error for binary constant weight codes we derive some bounds on the exponent of the probability of undetected error for binary constant weight codes these bounds enable us to extend the region in which the exponent of the probability of undetected error is exactly determined

linear block codes for error detection corresp the probability of undetected error of linear block codes for use on a binary symmetric channel is investigated upper hounds are derived several classes of linear block codes are proved to have good error detecting capability

bounds on the worst case probability of undetected error upper and lower bounds on the average worst case probability of undetected error for linear n k q codes are given

an algorithm for the bi criterion integer programming problem abstract we specify a variation of the weighting method for multi criterion optimization which determines nondominated solutions to the bi criterion integer programming problem the technique makes use of imposed constraints based on nondominated points for the bi criterion case we develop an algorithm which finds all nondominated points by solving a sequence of single criterion integer programming problems we present computational results for the linear 0 1 case and discuss the extension of our algorithm to the general multi criterion integer programming problem

almost mds and near mds codes for error detection the error detection capability of almost mds amds and nearly mds nmds codes is studied necessary and sufficient conditions for the codes to be proper or good for error detection are given

an interactive procedure using domination cones for bicriterion shortest path problems abstract in this paper an interactive procedure is developed for the bicriterion shortest path problem it is assumed that the decision maker s inherant utility function is quasi concave and non increasing and that the network consists of non negative integer valued arc lengths the proposed procedure uses the concept of domination cones which it develops from pairwise comparisons of alternatives these domination cones are used to fathom a large number of pareto optimal solutions extensive computational testing was performed on large grid networks simulating the decision maker s response using polynomial utility functions the results indicate that our proposed procedure is able to converge to the optimal solution in a reasonably small number of pairwise comparisons even for those problems with a large number of pareto optimal solutions

a class of practical interactive branch and bound algorithms for multicriteria integer programming abstract a practical interactive solution approach to multicriteria integer programming problems is developed the problem is solved by a branch and bound method that employs the zionts and wallenius procedure 23 for solving the multicriteria linear programming problem the development of algorithms for multicriteria decision problems itself is a multicriteria problem which involves the simultaneous minimization of the number of questions asked of the decision maker and the solution time two branch and bound algorithms that follow different search strategies to meet different levels of these criteria have been developed further two families of hybrid algorithms that incorporate a combination of the strategies of the two algorithms have also been developed strategies for the exploration of the decision maker s preference structure are discussed computational experience with the algorithms is presented the class of algorithms represents a collection of viable solution strategies applicable to a variety of decision making styles

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

on testing for improper error detection codes a family of tests for improper codes is given these tests can be used in cases where the complete weight distribution of the code is unknown it was found that knowledge of the number of minimum weight codewords can be used to greatly increase the effectiveness of the asymptotic varshamov gilbert test further improvement is possible as more is known about the number of other weight codewords

finding efficient solutions for rectilinear distance location problems efficiently abstract given n planar existing facility locations a planar new facility location x is called efficient if there is no other location y for which the rectilinear distance between y and each existing facility is at least as small as between x and each existing facility and strictly less for at least one existing facility rectilinear distances are typically used to measure travel distances between points via rectilinear aisles or street networks we first present a simple arrow algorithm based entirely on geometrical analysis that constructs all efficient locations we then present a row algorithm which is of order n log n that constructs all efficient locations and establish that no alternative algorithm can be of a lower order

an overview of techniques for solving multiobjective mathematical programs multiobjective mathematical programming has been one of the fastest growing areas of or ms during the last 15 years this paper presents some reasons for the rapidly growing increase in interest in multiobjective mathematical programming a discussion of the advantages and disadvantages of the three general approaches articulation of the decision maker s preference structure over the multiple objectives prior to during or after the optimization towards multiobjective mathematical programming a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming and a discussion of important areas for further research the overview concentrates on those techniques which require an articulation of the decision maker s preference structure either during or after the optimization since these are the areas where most of the recent research has been conducted it differs from previous overviews in that in addition to the timing of the elicited preference informa

multi criteria branch and bound a vector maximization algorithm for mixed 0 1 multiple objective linear programming the paper describes the multi criteria branch and bound mcbb algorithm a vector maximization algorithm capable of deriving all efficient extreme points for small and medium sized mixed 0 1 multiple objective linear programming mixed 0 1 molp particular emphasis is given to computational aspects aiming principally at accelerating the solution procedure for facilitating the decision maker s search toward the most preferred efficient solution the notion of efficient combinations of the binary variables is further exploited it is also shown that the mcbb algorithm can be used in single objective problems mixed integer lp problems in order to determine all alternative optima as well as in mixed integer molp problems and pure 0 1 molp problems that frequently arise in practice a computational experiment is included in the paper in order to illustrate the performance of the algorithm

on the probability of undetected error for overextended reed solomon codes upper and lower bounds on the weight distribution of overextended reed solomon oers codes are derived from which tight upper and lower bounds on the probability of undetected error for oers codes are obtained for q ary symmetric channels