permutation arrays under the chebyshev distance an n d permutation array pa is a subset of sn with the property that the distance under some metric between any two permutations in the array is at least d they became popular recently for communication over power lines motivated by an application to flash memories in this paper the metric used is the chebyshev metric a number of different constructions are given as well as bounds on the size of such pa

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

spherical codes generated by binary partitions of symmetric pointsets several constructions are presented by which spherical codes are generated from groups of binary codes in the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line the main ideas are code concatenation and set partitioning extensive tables are presented for spherical codes in dimension n spl les 24

the generation of n n n 1 n 1 permutation group codes for communication systems this paper concerns the construction and hardware execution of n n n 1 n 1 permutation group codes pgcs for communication systems cyclic shift techniques acting on a permutation including cyclic shift operators and their compound functions cfs are defined and demonstrated then compared to other tools such as cyclic subgroups and n dimension cyclic shift registers a generalized finite state machine is established that can enumerate n permutations based on complete cfs this is a hardware oriented algorithm that is capable of being significantly faster than all existing algorithms which we can find up to now after this the ideal structural features for an ordered set of n permutations are discussed and the multiset features of n n n 1 n 1 pgcs in this ordered set are pinpointed a simpler way of generating n n n 1 n 1 pgcs is then developed using cyclic shift techniques where the code length n is a prime this outperforms existing approaches using composite operation and affine transform on module n operation the simulation experiments in awgn channel show that the performance on codeword error rates wer and signal noise ratio snr becomes better as the code length increases and the best snr performance achieves 0 8 db at 10 5 wer for code length n 11

the r hamming gap and distance gap preserving mappings from binary vectors to permutations abstract the well known hamming distance between a pair of permutations or strings of the same length is simply the number of pairs of different digits in these permutations it has been an interesting topic of research to find mappings from the binary vectors to permutations of the same length such that the hamming distance is preserved or increased as a natural variation we introduce the hamming gap of radius r between two permutations which is in a way equivalent to the number of digits where the corresponding pair of entries differ by at least r this is called the r hamming gap we first discuss the properties of this new concept we then show mappings from binary vectors to permutations such that the images of a pair of binary vectors at hamming distance d have r hamming gap at least d we also show the generalization of our findings to permutations on z n where n 0 instead of n

lp decodable multipermutation codes in this paper we introduce a new way of constructing and decoding multipermutation codes multipermutations are the permutations of a multiset that generally consist of duplicate entries we first introduce a class of binary matrices called multipermutation matrices each of which corresponds to a unique and distinct multipermutation by enforcing a set of linear constraints on these matrices we define a new class of codes that we term linear program lp decodable multipermutation codes in order to decode these codes using an lp thereby enabling soft decoding we characterize the convex hull of multipermutation matrices this characterization allows us to relax the coding constraints to a polytope and to derive two lp decoding problems these two problems are respectively formulated by relaxing the maximum likelihood decoding problem and the minimum chebyshev distance decoding problem because these codes are non linear we also study efficient encoding and decoding algorithms we first describe an algorithm that maps consecutive integers one by one to an ordered list of multipermutations based on this algorithm we develop an encoding algorithm for a code proposed by shieh and tsai a code that falls into our class of lp decodable multipermutation codes regarding decoding algorithms we propose an efficient distributed decoding algorithm based on the alternating direction method of multipliers finally we observe from the simulation results that the soft decoding techniques we introduce can significantly outperform hard decoding techniques that are based on quantized channel outputs

interior point decoding for linear vector channels based on convex optimization in the present paper a novel decoding algorithm for low density parity check ldpc codes based on convex optimization is presented the decoding algorithm which is referred to hereinafter as interior point decoding is designed for linear vector channels the linear vector channels include several practically important channels such as inter symbol interference channels and partial response pr channels it is shown that the maximum likelihood decoding mld rule for a linear vector channel can be relaxed to a convex optimization problem which is called a relaxed mld problem the proposed decoding algorithm is based on a numerical optimization technique known as the interior point method with barrier functions approximate variations of an interior point method based on the gradient descent and newton methods are used to solve the relaxed mld problem compared with a conventional joint message passing decoder from computer simulations it is observed that the proposed decoding algorithm achieves better ber performance on pr channels with less decoding complexity in several cases furthermore an extension of the proposed algorithm for high order modulation formats such as pam and qam is presented

permutation codes for the gaussian channel the initial vector problem is considered for group codes for the gaussian channel and in particular for codes generated by permutation groups variant i and variant ii permutation codes are defined and optimal initial vectors for these codes are constructed a numerical algorithm for constructing optimal group codes is presented together with examples of this algorithm applied to several permutation groups

games with discontinuous payoffs a strengthening of reny s existence theorem we provide a pure nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of reny 1999 in comparison with reny s argument our proof is brief our result subsumes a prior existence result of reny 1999 that is not covered by his theorem we use the main result to prove the existence of pure nash equilibrium in a class of finite games in which agents pure strategies are subsets of a given set and in turn use this to prove the existence of stable configurations for games similar to those used by schelling 1971 1972 to study residential segregation in which agents choose locations

on ensembles of low density parity check codes asymptotic distance distributions we derive expressions for the average distance distributions in several ensembles of regular low density parity check codes ldpc among these ensembles are the standard one defined by matrices having given column and row sums ensembles defined by matrices with given column sums or given row sums and an ensemble defined by bipartite graphs

using graphs for the analysis and construction of permutation distance preserving mappings a new way of looking at permutation distance preserving mappings dpms is presented by making use of a graph representation the properties necessary to make such a graph distance preserving are also investigated further this new knowledge is used to analyze previous constructions as well as to construct a new general mapping algorithm for a previous multilevel construction

bat chirps with good properties zak space construction of perfect polyphase sequences previously a discretization of the linear fm chirp of length n kl 2 l and kl isin z was given and the conditions for its minimal zak space support were derived chirps satisfying these conditions are known as finite chirps in this work subsets of finite chirps of length n l 2 l a prime are examined the investigation leads to a new zak space construction of general polyphase sequence sets of size l 1 with optimal auto and cross correlation properties known as perfect sequence sets it is shown that perfect sequence sets are closely related to sets of finite chirps and in particular include the sets of zadoff chu sequences which are identical with subsets of finite chirps and the sets of generalized frank sequences which are identical with sets of modulations of finite chirps as special cases the entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group the construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group

ulam ball size analysis for permutation and multipermutation codes correcting translocation errors permutation and multipermutation codes in the ulam metric have been suggested for use in non volatile memory storage systems such as flash memory devices in this paper we introduce a new method to calculate permutation ball sizes in the ulam metric using young tableaux and prove the non existence of non trivial perfect permutation codes in the ulam metric we then extend the study to multipermutations providing upper and lower bounds on multipermutation ulam ball sizes and resulting upper and lower bounds on the maximal size of multipermutation codes in the ulam metric

a note on the optimality of variant i permutation modulation codes in this correspondence the optimality of variant i permutation codes initially proposed by slepian see proc ieee vol 53 no 3 p 228 236 mar 1965 is shown in a simple way

a generalized upper bound and a multilevel construction for distance preserving mappings a new general upper bound is derived on the sum of the hamming distances between sequences when mapping from one set of sequences to another it is shown that a similar upper bound for mappings from binary sequences to permutation sequences is a special case of this upper bound and this is used to evaluate known mappings also new distance preserving mappings dpms from binary sequences to permutation sequences are presented based on a multilevel construction in addition to explicit distance conserving mappings distance increasing and distance reducing mappings are also presented several of the new dpms attain the upper bound

lp decodable permutation codes based on linearly constrained permutation matrices a set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes the main feature of this class of permutation codes called linear programming lp decodable permutation codes is this lp decodability it is demonstrated that the lp decoding performance of the proposed class of permutation codes is characterized by the vertices of the code polytope of the code two types of linear constraints are discussed one is structured constraints and the other is random constraints the structured constraints allow an efficient encoding algorithm on the other hand the random constraints enable us to use probabilistic methods for analyzing several code properties such as the average cardinality and the average weight distribution

distance increasing maps of all lengths by simple mapping algorithms distance increasing maps from binary vectors to permutations namely dims are useful for the construction of permutation arrays while a simple mapping algorithm defining dims of even lengths is known existing dims of odd lengths are defined either by recursively merging dims of shorter lengths or by complicated mapping algorithms in this paper simple mapping algorithms defining dims of all lengths are presented

on the geometry of the inhomogeneous heisenberg ferromagnet nonintegrable case new classes of exact solutions of the inhomogeneous heisenberg ferromagnet equation are found by means of a geometrical technique this technique consists of calculating one parameter families of geodesics on surfaces in e3 the solutions correspond to geodesics on surfaces of rotation

on integrability of the inhomogeneous heisenberg ferromagnet model examination of a new test we present an improved version of the integrability test based on application of lie point transformations acting on the bare linear problem the test is then applied to the inhomogeneous heisenberg ferromagnet model equation the integrable cases selected by this test are identical with those obtained by the standard painleve test

representing group codes as permutation codes given an abstract group spl gscr an n dimensional orthogonal matrix representation g of spl gscr and an initial vector x spl isin r sup n slepian defined the group code generated by the representation g to be the set of vectors gx if g is a group of permutation matrices the set gx is called a permutation code for permutation codes a stack algorithm decoder exists that in the presence of low noise produces the maximum likelihood estimate of the transmitted vector by using far fewer computations than the standard decoder in this correspondence a new concept of equivalence of codes of different dimensions is presented which is weaker than the usual definition of equivalent codes we show that every group code is weakly equivalent to a permutation code and we discuss the minimal degree of this permutation code

surface embeddability approach to the dynamics of the inhomogeneous heisenberg spin chain the surface embeddability approach of lund and regge is applied to the classical inhomogeneous heisenberg spin chain to study the class of inhomogeneity functions f for which the spin evolution equation and its gauge equivalent generalized nonlinear schrodinger equation gnlse are exactly solvable writing the spin vector s x t as xr and identifying r x t with a position vector generating a surface we show that the kinematic equation satisfied by r implies certain constraints on the admissible geometries of this surface these constraints together with the gauss mainardi codazzi equations enable us to express the coefficient of the second fundamental form as well as f in terms of the metric coefficients g and its derivatives for arbitrary time independent g explicit solutions for the gnlse can also be found in terms of the same quantities of the admissible surfaces generated by r a special class that emerges naturally is that of surfaces of revolution explicit solutions for r and s are found

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

distance preserving and distance increasing mappings from ternary vectors to permutations permutation arrays have found applications in powerline communication one construction method for permutation arrays is to map good codes to permutations using a distance preserving mappings dpm dpms are mappings from the set of all q ary vectors of a fixed length to the set of permutations of some fixed length the same or longer such that every two distinct vectors are mapped to permutations with the same or larger hamming distance than that of the vectors a dpm is called distance increasing dim if the distances are strictly increased except when the two vectors are equal in this correspondence we propose constructions of dpms and dims from ternary vectors the constructed dpms and dims improve many lower bounds on the maximal size of permutation arrays

codes in permutations and error correction for rank modulation codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors we study basic coding theoretic problems for such codes representing them as subsets of the set of permutations of n elements equipped with the kendall tau distance we derive several lower and upper bounds on the size of codes these bounds enable us to establish the exact scaling of the size of optimal codes for large values of n we also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors

on the labeling problem of permutation group codes under the infinity metric we consider codes over permutations under the infinity norm given such a code we show that a simple relabeling operation which produces an isomorphic code may drastically change the minimal distance of the code thus we may choose a code structure for efficient encoding procedures and then optimize the code s minimal distance via relabeling to establish that the relabeling problem is hard and is of interest we formally define it and show that all codes may be relabeled to get a minimal distance at most 2 on the other hand the decision problem of whether a code may be relabeled to distance 2 or more is shown to be np complete and calculating the best achievable minimal distance after relabeling is proved to be hard to approximate up to a factor of 2 we then consider general bounds on the relabeling problem we specifically construct the optimal relabeling for transitive cyclic groups we conclude with the main result a general probabilistic bound which we then use to show both the agl p group and the dihedral group on p elements may be relabeled to a minimal distance of p o p in p

an improvement on the gilbert varshamov bound for permutation codes permutation codes have been shown to be useful in power line communications block ciphers and multilevel flash memory models construction of such codes is extremely difficult in fact the only general lower bound known is the gilbert varshamov type bound in this paper we establish a connection between permutation codes and independent sets in certain graphs using the connection we improve the gilbert varshamov bound asymptotically by a factor log n when the code length n goes to infinity

hadamard well posedness of the α core abstract in this paper we discuss the continuity property of the core with respect to data perturbations in different environments we show that some collections of abstract economies or normal games with the nonempty core have the hadamard well posedness property we also show that the core points of every game in a dense residual subset are essential

constant composition codes as subcodes of cyclic codes constant composition codes are codes where the frequency distribution of the elements in a codeword is the same for all codewords in this paper three classes of constant composition codes are constructed these codes are subcodes of cyclic codes which have few weights occurring among the codewords the new codes are excellent asymptotically compared to the previously best known constant composition codes

optimal nonuniform signaling for gaussian channels variable rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied when the criterion is one of minimizing the average transmitted energy for a given average bit rate the best possible distribution with which to select constellations points is a maxwell boltzmann distribution in principle when constellation points are selected according to a maxwell boltzmann distribution the ultimate shaping gain pi e 6 or 1 53 db can be achieved in any dimension nonuniform signaling schemes can be designed by mapping simple variable length prefix codes onto the constellation using the huffman procedure prefix codes can be designed that approach the optimal performance these schemes provide a fixed rate primary channel and a variable rate secondary channel and are easily incorporated into standard lattice type coded modulation schemes

optimal constant composition codes from zero difference balanced functions constant composition codes are a special class of constant weight codes and include permutation codes as a subclass they have applications in communications engineering in this correspondence a generic construction of optimal constant composition codes using zero difference balanced functions is introduced it generalizes the earlier construction of optimal constant composition codes employing perfect nonlinear functions in addition two classes of optimal constant composition codes with new parameters are reported

a construction of permutation codes from rational function fields and improvement to the gilbert varshamov bound due to recent applications to communications over powerlines multilevel flash memories and block ciphers permutation codes have received a lot of attention from both coding and mathematical communities one of the benchmarks for good permutation codes is the gilbert varshamov bound although there have been several constructions of permutation codes the gilbert varshamov bound still remains to be the best asymptotical lower bound except for a recent improvement in the case of constant minimum distance in this paper we present an algebraic construction of permutation codes from rational function fields and it turns out that for a prime number n of a symbol length this class of permutation codes improves the gilbert varshamov bound by a factor n asymptotically for a minimum distance d with d o sqrt n furthermore for a constant minimum distance d we improve the gilbert varshamov bound by a factor n as well as the recent one given by gao et al by a factor n log n asymptotically for all sufficiently large n

nonlocal symmetries and a working algorithm to isolate integrable geometries a 1 parameter group of nonlocal symmetries of nonhomogeneous nonlinear schrodinger system with the coupling function linear in x is presented on using this symmetry the author is able to insert the spectral parameter into the nonparametric lax pair in all cases which are known to be integrable a working algorithm to isolate integrable geometries proposed by levi sym and tu 1990 is extended

limited magnitude error correcting gray codes for rank modulation we construct error correcting codes over permutations under the infinity metric which are also gray codes in the context of rank modulation i e are generated as simple circuits in the rotator graph these errors model limited magnitude or spike errors for which only single error detecting gray codes are currently known surprisingly the error correcting codes we construct achieve a better asymptotic rate than that of presently known constructions not having the gray property and exceed the gilbert varshamov bound additionally we present efficient ranking and unranking procedures as well as a decoding procedure that runs in linear time finally we also apply our methods to solve an outstanding issue with error detecting rank modulation gray codes also known in this context as snake in the box codes under a different metric the kendall tau metric in the group of permutations over an even number of elements s 2n where we provide asymptotically optimal codes

distance increasing mappings from binary vectors to permutations mappings from the set of binary vectors of a fixed length to the set of permutations of the same length that strictly increase hamming distances except when that is obviously not possible are useful for the construction of permutation codes in this correspondence we propose recursive and explicit constructions of such mappings some comparisons show that the new mappings have better distance expansion distributions than other known distance preserving mappings dpms we also give some examples to illustrate the applications of these mappings to permutation arrays pas

a note on the equilibrium existence problem in discontinuous games in this note we prove an equilibrium existence theorem for games with discontinuous payoffs and convex and compact strategy spaces it generalizes the classical result of reny 1999 as well as the recent paper of mclennan monteiro and tourky 2011 our conditions are simple and easy to verify importantly examples of spatial location models show that our conditions allow for economically meaningful payoff discontinuities that are not covered by other conditions in the literature

an algebraic method to construct the darboux matrix we present an effective procedure to construct the 1 soliton darboux matrix our approach based on the zakharov shabat mikhailov s dressing method is especially useful in the case of non canonical normalization and for non isospectral linear problems the construction is divided into two steps first we represent a given linear problem as a system of some algebraic constraints on two matrices in this context we introduce and discuss invariants of the darboux matrix second we derive the darboux matrix demanding that it preserves the algebraic constraints in particular we consider in details the restrictions imposed by various reduction groups on the form of the darboux matrix

decoding spherical codes for the gaussian channel a decoding algorithm for permutation codes that is equivalent to maximum likelihood decoding but less complex than the correlation decoder is presented a general construction for iteratively maximum likelihood decodable imld codes is proved and used to construct imld codes for every dimension n d slepian 1965 defined permutation modulation codes and presented an efficient algorithm for their decoding slepian s decoding scheme is one of the principal components of the permutation code decoding algorithm presented

continuity properties of the nash equilibrium correspondence in a discontinuous setting abstract we introduce a new complete metric space of discontinuous normal form games and prove that the nash equilibrium correspondence is upper semicontinuous with non empty and compact values so using the theorem of fort 1949 we obtain that the correspondence is also lower semicontinuous in a dense subset we introduce new topological assumptions on the payoff functions and a strengthening of standard quasi concavity properties examples show that our results cannot be obtained from the previous ones

line codes generated by finite coxeter groups using an algebraic approach based on the theory of coxeter groups we design and describe the performance of a class of line codes derived from permutation modulation useful for parallel transmission of b bits over b 1 wires and admitting especially simple encoding and decoding algorithms with these codes resistance to common mode noise is obtained by using codewords whose components sum to zero simultaneous switching output noise is reduced by using constant energy signals and the effects of intersymbol interference are reduced by having decisions based on only two values at the input of the final slicers codebook design is based on the theory of group codes for the gaussian channel as specialized to coxeter matrix groups generated by reflections in orthogonal hyperplanes a number of designs are exhibited some of them being novel or improving on previously obtained codes

distance increasing mappings from binary vectors to permutations that increase hamming distances by at least two in this correspondence for any k ges 2 we first propose two constructions of n k distance increasing mappings dims from the set of binary vectors of length n to the set of permutations of the same length that strictly increase the hamming distance by at least k except when it is obviously not possible next we prove that for any k ges 2 there is a smallest positive integer nk such that an n k dim can be constructed for any n ges nk an explicit upper bound on nk is also given

constructions of permutation arrays a permutation array pa of length n and minimum distance d is a set of permutations of n elements such that any two permutations coincide in at most n d positions some constructions of pas are given

combinatorial constructions of optimal constant composition codes constant composition codes cccs are a special class of constant weight codes they include permutation codes as a subclass in this correspondence a link between cccs and generalized double resolvable packing designs is developed and used to construct several infinite series of optimal cccs

correcting limited magnitude errors in the rank modulation scheme we study error correcting codes for permutations under the infinity norm motivated by a novel storage scheme for flash memories called rank modulation in this scheme a set of n flash cells are combined to create a single virtual multilevel cell information is stored in the permutation induced by the cell charge levels spike errors which are characterized by a limited magnitude change in cell charge levels correspond to a low distance change under the infinity norm we define codes protecting against spike errors called limited magnitude rank modulation codes lmrm codes and present several constructions for these codes some resulting in optimal codes these codes admit simple recursive and sometimes direct encoding and decoding procedures we also provide lower and upper bounds on the maximal size of lmrm codes both in the general case and in the case where the codes form a subgroup of the symmetric group in the asymptotic analysis the codes we construct outperform the gilbert varshamov like bound estimate

new distance preserving maps of odd length we propose a new construction of maps preserving the hamming distance from the set of binary vectors of odd length to the set of permutations of the same length we investigate their distance increasing property and show that a class of new maps have better distance increasing property than previously known maps of equal length

stochastic power control for wireless networks via sdes probabilistic qos measures the power control of wireless networks is formulated using a stochastic optimal control framework in which the evolution of the channel is described by stochastic differential equations sdes the latter capture the spatio temporal variations of the communication link as well as the randomness this class of models is more realistic than the static models usually encountered in the literature under this scenario average and probabilistic quality of service qos measures are introduced to evaluate the performance of any control strategy by using chernoff bounds moreover the chernoff bound is computed explicitly while the solution of the stochastic optimal power control is obtained through pathwise optimization the pathwise optimization can be solved using linear programming if predictable control strategies are introduced finally if predictable control strategies do not hold it is shown that the proposed power control problem reduces to particular convex optimizations

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

reciprocal upper semicontinuity and better reply secure games a comment a convex compact and possibly discontinuous better reply secure game has a nash equilibrium we introduce a very weak notion of continuity that can be used to establish that a game is better reply secure and we show that this notion of continuity is satisfied by a large class of games the class of better reply secure games was introduced by reny 1999 who showed the existence of a pure nash equilibrium for games in this class furthermore reny provided two conditions that when combined become suf ficient for a game to be better reply secure the first condition is payoff secu rity which means that given a joint strategy x every player can find a strategy that yields almost the same payoff at x even when the other players slightly deviate from x the second condition is reciprocal upper semicontinuity rusc this condition roughly speaking requires the payoff of one of the players to jump up whenever the payoff of another player jumps down we introduce the notion of weak reciprocal upper semicontinuity wrusc a strict weakening of rusc and prove that a game that is wrusc and payoff secure is better reply secure and therefore has a pure strategy nash equilibrium

error correction in flash memories via codes in the ulam metric we consider rank modulation codes for flash memories that allow for handling arbitrary charge drop errors unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements the proposed translocation rank codes account for more general forms of errors that arise in storage systems translocations represent a natural extension of the notion of adjacent transpositions and as such may be analyzed using related concepts in combinatorics and rank modulation coding our results include derivation of the asymptotic capacity of translocation rank codes construction techniques for asymptotically good codes as well as simple decoding methods for one class of constructed codes as part of our exposition we also highlight the close connections between the new code family and permutations with short common subsequences deletion and insertion error correcting codes for permutations and permutation codes in the hamming distance

permutation arrays for powerline communication and mutually orthogonal latin squares we develop a connection between permutation arrays that are used in powerline communication and well studied combinatorial objects mutually orthogonal latin squares mols from this connection many new results on permutation arrays can be obtained

algebraic constructions of constant composition codes constant composition codes are a special class of constant weight codes they include permutation codes as a subclass in this correspondence two classes of optimal constant composition codes are constructed both constructions employ perfect nonlinear functions but they are different

optimized permutation modulation permutation modulation is a class of group codes for the gaussian channel a group code is a set of vectors obtained by a group of orthogonal matrices operating on an initial vector an important problem is to find the initial vector yielding the largest minimum euclidean distance between two vectors this problem is solved for permutation modulation the performance of such optimized permutation modulation is analyzed compared to binary antipodal signals and psk phase shift keying it typically requires 2 5 4 db less energy for the same minimum distance

optimal permutation codes for the gaussian channel this correspondence contains a continuation of the table contained in karlof 1989 listing the minimum distance of optimal permutation codes generated by primitive permutation groups of degree less than or equal to 20 we use a nonlinear programming algorithm developed using geometric programming techniques

group codes generated by finite reflection groups slepian type group codes generated by finite coxeter groups are considered the resulting class of group codes is a generalization of the well known permutation modulation codes of slepian 1965 it is shown that a restricted initial point problem for these codes has a canonical solution that can easily be computed this allows one to enumerate all optimal group codes in this restricted sense and essentially solves the initial point problem for all finite reflection groups formulas for the cardinality and the minimum distance of such codes are given the new optimal group codes from exceptional reflection groups that are obtained achieve high rates and have excellent distance properties the decoding regions for maximum likelihood ml decoding are explicitly characterized and an efficient ml decoding algorithm is presented this algorithm relies on an extension of slepian s decoding of permutation modulation and has similar low complexity

cyclic constructions of distance preserving maps distance preserving maps dpms from binary vectors to permutations are useful for the construction of permutation arrays a new construction of dpms is presented we study the distance increasing property of the new dpms that this construction yields then we show that new dpms contain a class of nicely structured dpms of even length with good distance increasing property

existence of strong equilibrium in discontinuous games abstract in this paper we give necessary and sufficient conditions for the existence of strong equilibria in games with non ordered preferences our result does not require continuous preferences and in the case of normal form games quasi concavity of payoff functions is not needed the result has been obtained by using the ky fan minimax inequality examples illustrate our conditions in some economic situations and compare the result with the previous literature