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

lattice coding and decoding achieve the optimal diversity multiplexing tradeoff of mimo channels this paper considers communication over coherent multiple input multiple output mimo flat fading channels where the channel is only known at the receiver for this setting we introduce the class of lattice space time last codes we show that these codes achieve the optimal diversity multiplexing tradeoff defined by zheng and tse under generalized minimum euclidean distance lattice decoding our scheme is based on a generalization of erez and zamir mod lambda scheme to the mimo case in our construction the scalar scaling of erez zamir and costa gaussian dirty paper schemes is replaced by the minimum mean square error generalized decision feedback equalizer mmse gdfe this result settles the open problem posed by zheng and tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity multiplexing tradeoff moreover our results shed more light on the structure of optimal coding decoding techniques in delay limited mimo channels and hence open the door for novel approaches for space time code constructions in particular 1 we show that mmse gdfe plays a fundamental role in approaching the limits of delay limited mimo channels in the high signal to noise ratio snr regime unlike the additive white gaussian noise awgn channel case and 2 our random coding arguments represent a major departure from traditional space time code designs based on the rank and or mutual information design criteria

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

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

optimal entanglement criterion for mixed quantum states we develop a strong and computationally simple entanglement criterion the criterion is based on an elementary positive map phi which operates on state spaces with even dimension n or 4 it is shown that phi detects many entangled states with a positive partial transposition ppt and that it leads to a class of optimal entanglement witnesses this implies that there are no other witnesses which can detect more entangled ppt states the map phi yields a systematic method for the explicit construction of high dimensional manifolds of bound entangled states

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

stock market dynamics abstract we elucidate on several empirical statistical observations of stock market returns moreover we find that these properties are recurrent and are also present in invariant measures of low dimensional dynamical systems thus we propose that the returns are modeled by the first poincare return time of a low dimensional chaotic trajectory this modeling which captures the recurrent properties of the return fluctuations is able to predict well the evolution of the observed statistical quantities in addition it explains the reason for which stocks present simultaneously dynamical properties and high uncertainties in our analysis we use data from the s p 500 index and the brazilian stock telebras

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

bounds for codes over the unit circle let c be a code of length n and rate r over the alphabet a q exp 2 pi ir q r o 1 cdots q 1 and let d c be the minimum euclidean distance of c for large n the lower and upper bounds are obtained in parametric form on the achievable pairs r delta where delta d 2 c n holds to obtain these bounds the arguments leading to the gilbert bound and the elias bound respectively are applied to the alphabet a q for q rightarrow infty they are shown to be expressible in terms of the modified bessel function of the first kind the elias type bound is compared with the kabatyanskii levenshtein k l bound that holds for less restrictive alphabets it turns out that our upper bound improves the k l bound for delta leq 0 93

tables of sphere packings and spherical codes the theta function of a sphere packing gives the number of centers at each distance from the origin the theta functions of a number of important packings a n d n e n the leech lattice and others and tables of the first fifty or so of their coefficients are given in this paper

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

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

scaling of swimming sequences in copepod behavior data analysis and simulation abstract we consider symbolic sequences of copepod behavior classified as break and slow swimming states successive residence times for each state have been recorded for 327 symbolic times series obtained from 52 different trajectories we performed a symbolic dynamics analysis of the succession of states and showed that the probability densities of the duration of each state obey power laws for large times we analyzed the transition between states and showed as expected the non markovian properties of this dynamics we further simulate a copepod trajectory using an alternate renewal process for the generation of the sequence time series and using a brownian motion for the copepod motion during swimming periods

free electron gas in the apollonian network multifractal energy spectrum and its thermodynamic fingerprints we study the free electron gas in an apollonian network within the tight binding framework the scale free and small world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities gaps and minibands after an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum the fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat the absence of chiral symmetry of the apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations

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

concurrence of arbitrary dimensional bipartite quantum states we derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension a functional relation is established relating concurrence the peres horodecki criterion and the realignment criterion we demonstrate that our bound is exact for some mixed quantum states the significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states some of which fail to be identified by the usual concurrence estimation method

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

generalising wigner s theorem we analyse linear maps of operator algebras mapping the set of rank k projectors onto the set of rank l projectors surjectively a complete characterisation of such maps for prime is provided a particular case corresponding to is well known as wigner s theorem hence our result may be considered as a generalisation of this celebrated wigner s result

joint source channel codes for mimo block fading channels we consider transmission of a continuous amplitude source over an l block rayleigh fading mt x mr multiple input multiple output mimo channel when the channel state information is only available at the receiver since the channel is not ergodic shannon s source channel separation theorem becomes obsolete and the optimal performance requires a joint source channel approach our goal is to minimize the expected end to end distortion particularly in the high signal to noise ratio snr regime the figure of merit is the distortion exponent defined as the exponential decay rate of the expected distortion with increasing snr we provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths for the lower bounds we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital analog transmission in each case by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio we prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom that is l 1 and min mt mr 1 when we have more degrees of freedom our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio we demonstrate that our results which were derived for a complex gaussian source can be extended to more general source distributions as well

m ary balanced codes with parallel decoding an m ary block code m 2 3 4 ldots of length n in mathbf i mathbf i mskip 7mu mathbf n is called balanced if and only if every codeword is balanced that is the real sum of the codeword components or weight is equal to left lfloor m 1 n 2 right rfloor this paper presents efficient encoding schemes to m ary balanced codes with parallel hence fast decoding in fact the decoding time complexity is o 1 digit operations these schemes are a generalization to the m ary alphabet of knuth s complementation method with parallel decoding let binom n w m indicate the number of m ary words of length n and weight w in 0 1 ldots m 1 n for any m in mathbf i mathbf i mskip 7mu mathbf n m geq 2 a simple implementation of the method is given which uses r in mathbf i mathbf i mskip 7mu mathbf n check digits to balance k leq binom r left lfloor m 1 r 2 right rfloor vphantom r r m m bmod 2 m 1 k bmod 2 m 1 information digits with an encoding time complexity of o mk log m k digit operations a refined implementation of the parallel decoding method is also given with r check digits and k leq m r 1 m 1 information digits where the encoding time complexity is o k sqrt log m k thus the proposed codes are less redundant than the m ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

fractal and multifractal properties of exit times and poincarerecurrences systems with chaotic dynamics possess anomalous statistical properties and their trajectories do not correspond to the gaussian process this property imposes description of such time characteristics as the distribution of exit times or poincar acute e recurrences by introducing a multi fractal time scale in order to satisfy the observed powerlike tails of the distributions we introduce a corresponding phase space time partitioning and spectral function for dimensions and make a connection between dimensions and transport exponent that defines the anomalous open quotes strange close quotes kinetics copyright ital 1997 ital the american physical society

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

reflection group codes and their decoding this paper builds on mittelholzer and lahtonen s study of group codes for the gaussian channel based on reflection groups a careful analysis of the action of a reflection group on its roots leads to the development of improved methods for encoding and decoding the new algorithm is proved to achieve maximum likelihood decoding the complexity of decoding is analyzed and it is shown that a proper choice of the sequence of subgroups used in the algorithm can yield significant gains in the efficiency of decoding

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

group divisible codes and their application in the construction of optimal constant composition codes of weight three the concept of group divisible codes a generalization of group divisible designs with constant block size is introduced in this paper this new class of codes is shown to be useful in recursive constructions for constant weight and constant composition codes large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant composition codes of weight three and specified distance leaving only four cases undetermined previously the sizes of constant composition codes of weight three were known only for those of sufficiently large length

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

recurrence time analysis long term correlations and extreme events the recurrence times between extreme events have been the central point of statistical analyses in many different areas of science simultaneously the poincar e recurrence time has been extensively used to characterize nonlinear dynamical systems we compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series in particular we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function on the interval whereto the recurrences are observed and on the temporal correlations of time series in the case of long term correlations we verify the validity of the stretched exponential distribution which is uniquely defined by the exponent ensuremath gamma at the same time showing that it is restricted to the class of linear long term correlated processes simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different ensuremath gamma which shows a lack of invariance under the change of observables

upper bounds on the minimum distance of spherical codes we use linear programming techniques to obtain new upper bounds on the maximal squared minimum distance of spherical codes with fixed cardinality functions q sub j n s are introduced with the property that q sub j n s m if and only if the levenshtein bound l sub m n s on a n s max w w is an n w s code can be improved by a polynomial of degree at least m 1 general conditions on the existence of new bounds are presented we prove that for fixed dimension n spl ges 5 there exists a constant k k n such that all levenshtein bounds l sub m n s for m spl ges 2k 1 can be improved an algorithm for obtaining new bounds is proposed and discussed

further results on entanglement detection and quantification from the correlation matrix criterion the correlation matrix cm criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions it has been shown that it can be stronger than the positive partial transpose ppt criterion as well as the computable cross norm or realignment ccnr criterion in different situations however it remained as an open question whether there existed sets of states for which the cm criterion could be stronger than both criteria simultaneously here we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the ppt and ccnr criteria whose entanglement is revealed by the cm condition we also show that the cm can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general mixed states

the closest packing of equal circles on a sphere the closest packing of x circles on the surface of a sphere is examined with the use of techniques that have been developed to determine the stereochemical arrangement of atoms packed around a central atom the technique is based on the concept that the centres of the circles repel one another and minimizing the total repulsion energy leads to an approximate structure from which exact solutions can be determined a number of improved packings have been discovered for values of x in the range 20 40 many different types of structure are found that are of lower symmetries than those previously described the packing density p defined as the fraction of the spherical surface that is enclosed by the circles is found to increase as the number of circles increases in contrast to the conclusion from previous studies however this increase in p is very slight and the values remain substantially below that for an infinite number of circles or a close packed plane

state space structure and entanglement of rotationally invariant spin systems we investigate the structure of so 3 invariant quantum systems which are composed of two particles with spins j1 and j2 the states of the composite spin system are represented by means of two complete sets of rotationally invariant operators namely by the projections pj onto the eigenspaces of the total angular momentum j and by certain invariant operators qk which are built out of spherical tensor operators of rank k it is shown that these representations are connected by an orthogonal matrix whose elements are expressible in terms of wigner s 6 j symbols the operation of the partial time reversal of the combined spin system is demonstrated to be diagonal in the qk representation these results are employed to obtain a complete characterization of spin systems with j1 1 and arbitrary j2 1 we prove that the peres horodecki criterion of positive partial transposition ppt is necessary and sufficient for separability if j2 is an integer while for half integer spins j2 there always exist entangled ppt states bound entanglement we construct an optimal entanglement witness for the case of half integer spins and design a protocol for the detection of entangled ppt states through measurements of the total angular momentum

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

scaling features of texts images and time series in the given paper we consider the scaling features of long letter sequences like human writings discretized images and discretized 3nancial data using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate di5erent scalings for large and small 6uctuations we discuss complex phenomena in the scaling behavior of partition functions in the case of high frequency dax future data c 2001 elsevier science b v all rights reserved

cyclotomic constructions of zero difference balanced functions with applications based on a recent work of ding wang and xiong we present some cyclotomic constructions of zero difference balanced zdb functions which interpret the previous construction proposed by cai zeng helleseth tang and yang the resulted zdb functions can be used to generate optimal constant composition codes and perfect difference systems of sets with new parameters

distortion bounds for broadcasting with bandwidth expansion we consider the problem of broadcasting a single gaussian source to two listeners over a gaussian broadcast channel with rho channel uses per source sample where rho 1 a distortion pair d1 d2 is said to be achievable if one can simultaneously achieve a mean squared error mse d1 at receiver 1 and d2 at receiver 2 the main result of this correspondence is an outer bound for the set of all achievable distortion pairs that is we find necessary conditions under which d1 d2 is achievable we then apply this result to the problem of point to point transmission over a gaussian channel with unknown signal to noise ratio snr and rho 1 we show that if a system must be optimal at a certain snrmin then asymptotically the system distortion cannot decay faster than o 1 snr as for achievability we show that a previously reported scheme due to mittal and phamdo 2002 is optimal at high snr we introduce two new schemes for broadcasting with bandwidth expansion combining digital and analog transmissions we finally show how a system with a partial feedback returning from the bad receiver to the transmitter and to the good receiver achieves a distortion pair that lies on the outer bound derived here

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

the pbd closure of constant composition codes we show an interesting pairwise balanced design pbd closure result for the set of lengths of constant composition codes whose distance and size meet certain conditions a consequence of this pbd closure result is that the size of optimal constant composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code as an application the sizes of several infinite families of optimal constant composition codes are derived in particular the problem of determining the size of optimal constant composition codes having distance four and weight three is solved for all lengths sufficiently large this problem was previously unresolved for odd lengths except for lengths seven and eleven

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

characterizing cerebrovascular dynamics with the wavelet based multifractal formalism abstract using the wavelet transform modulus maxima wtmm approach we study the dynamics of cerebral blood flow cbf in rats aiming to reveal responses of macro and microcerebral circulations to changes in the peripheral blood pressure we show that the wavelet based multifractal formalism allows quantifying essentially different reactions in the cbf dynamics at the level of large and small cerebral vessels we conclude that unlike the macrocirculation that is nearly insensitive to increased peripheral blood pressure the microcirculation is characterized by essential changes of the cbf complexity

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

separability criteria and bounds for entanglement measures employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems the separability criterion is based on a nondecomposable positive map which operates on state spaces with even dimension n 4 and leads to a class of nondecomposable optimal entanglement witnesses it is shown that the bounds derived here complement and improve the existing bounds obtained from the criterion of positive partial transposition and from the realignment criterion