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

generalized hamming weights of nonlinear codes and the relation to the z sub 4 linear representation we give a new definition of generalized hamming weights of nonlinear codes and a new interpretation connected with it these generalized weights are determined by the entropy length profile of the code we show that this definition characterizes the performance of nonlinear codes on the wire tap channel of type ii the new definition is invariant under translates of the code it satisfies the property of strict monotonicity and the generalized singleton bound we check the relations between the generalized weight hierarchies of z sub 4 linear codes and their binary image under the gray map we also show that the binary image of a z sub 4 linear code is a symmetric not necessarily rectangular code moreover if this binary image is a linear code then it admits a twisted squaring construction

nonbinary quantum codes we present several results on quantum codes over general alphabets that is in which the fundamental units may have more than two states in particular we consider codes derived from finite symplectic geometry assumed to have additional global symmetries from this standpoint the analogs of calderbank shor steane codes and of gf 4 linear codes turn out to be special cases of the same construction this allows us to construct families of quantum codes from certain codes over number fields in particular we get analogs of quadratic residue codes including a single error correcting code encoding one letter in five for any alphabet size we also consider the problem of fault tolerant computation through such codes generalizing ideas of gottesman see phys rev a vol 57 no 1 p127 37 1998

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

stabilizer quantum codes over the clifford algebra the key problem for constructing a stabilizer quantum code is how to create a set of generators for the stabilizer of the stabilizer quantum code i e check matrix in this paper we suggest an approach based on the clifford algebra to create the check matrix for the stabilizer quantum codes in the proposed approach the recursive relation of the matrix transform over the clifford algebra is employed to generate the check matrix with the proposed approach a quantum code with any length can be constructed easily especially some new codes which are impossible via previous approaches are constructed

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

code enumerators and tutte polynomials it is proved that the set of higher weight enumerators of a linear code over a finite field is equivalent to the tutte polynomial associated to the code an explicit expression for the tutte polynomial is given in terms of the subcode weights generalizations of these results are proved and are applied to codeword m tuples these general results are used to prove a very general macwilliams type identity for linear codes that generalizes most previous extensions of the macwilliams identity in addition a general and very useful matrix framework for manipulating weight and support enumerators of linear codes is presented

nonbinary stabilizer codes over finite fields one formidable difficulty in quantum communication and computation is to protect information carrying quantum states against undesired interactions with the environment to address this difficulty many good quantum error correcting codes have been derived as binary stabilizer codes fault tolerant quantum computation prompted the study of nonbinary quantum codes but the theory of such codes is not as advanced as that of binary quantum codes this paper describes the basic theory of stabilizer codes over finite fields the relation between stabilizer codes and general quantum codes is clarified by introducing a galois theory for these objects a characterization of nonbinary stabilizer codes over fq in terms of classical codes over fq 2 is provided that generalizes the well known notion of additive codes over f4 of the binary case this paper also derives lower and upper bounds on the minimum distance of stabilizer codes gives several code constructions and derives numerous families of stabilizer codes including quantum hamming codes quadratic residue codes quantum melas codes quantum bose chaudhuri hocquenghem bch codes and quantum character codes the puncturing theory by rains is generalized to additive codes that are not necessarily pure bounds on the maximal length of maximum distance separable stabilizer codes are given a discussion of open problems concludes this paper

asymptotically good quantum codes exceeding the ashikhmin litsyn tsfasman bound it is known that quantum error correction can be achieved using classical binary codes or additive codes over f sub 4 asymptotically good quantum codes have been constructed from algebraic geometry codes and a bound on spl delta r was computed from the tsfasman vladut zink bound of the theory of classical algebraic geometry codes in this correspondence by the use of a concatenation technique we construct a family of asymptotically good quantum codes exceeding the bound in a small interval

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

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

new quantum mds codes from negacyclic codes let q be an odd prime power based on classical negacyclic codes we construct two classes of quantum maximum distance separable mds codes with parameters q2 1 q2 2d 3 d q where q 1 mod 4 and 2 d q 1 is even and q2 1 2 q2 1 2 2d 2 d q where 3 d q is odd some of these quantum mds codes are new in the sense that their parameters are different from all the previously known ones

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

robustness of discrete time direct adaptive controllers the problem of preserving stability of discrete time adaptive controllers in spite of reduced order modeling and output disturbances is addressed in this paper conditions for global stability convergence of the tracking error with bounded signals are derived for a discrete time pole zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals following an input output perpective the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors respectively and its stability is studied using the sector stability and passivity theorems first the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure in this l 2 framework it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed loop transfer function verifies certain conicity conditions the convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed the results are further extended to a broader class of l infty disturbances and reference inputs

the weight hierarchy of some reducible cyclic codes the generalized hamming weights ghws of linear codes are fundamental parameters the knowledge of which is of great interest in many applications however to determine the ghws of linear codes is difficult in general in this paper we study the ghws for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases this is achieved by extending the idea of yang et al into higher dimension and by employing some interesting combinatorial arguments it shall be noted that these cyclic codes may have arbitrary number of nonzeros

multiple mode orthogonal frequency division multiplexing with index modulation orthogonal frequency division multiplexing with index modulation ofdm im performs transmission by considering two modes over ofdm subcarriers which are the null and the conventional m ary signal constellation the spectral efficiency se of the system however is limited since the null mode itself does not carry any information and the number of subcarrier activation patterns increases combinatorially in this paper a novel im scheme called multiple mode ofdm im mm ofdm im is proposed for ofdm systems to improve the se by conveying information through multiple distinguishable modes and their full permutations a practical and efficient mode selection strategy which is constrained on the phase shift keying quadrature amplitude modulation constellations is designed two efficient detectors that provide different tradeoffs between the error performance and detection complexity are also proposed the principle of mm ofdm im is further extended to the in phase and quadrature components of ofdm signals and the method of generating multiple modes from the m ary pulse amplitude modulation constellation for this modified scheme is also introduced bit error rate ber analyses are provided for the proposed schemes monte carlo simulations on ber corroborate the analyses and show that the proposed schemes appear as promising multi carrier transmission alternatives by outperforming the existing ofdm im counterparts

on the weight hierarchy of goethals codes over z sub 4 the rth generalized hamming weight d sub r m j of the goethals code spl gscr sub m j of length 2 sup m over z sub 4 is considered in this correspondence in the case that m spl ges 3 is an odd integer d sub r m j is exactly determined for r 0 5 1 1 5 2 2 5 and 3 0 for a composite m we give an upper bound d sub r m j using the lifting technique

new upper bounds on generalized weights we derive new asymptotic upper bounds on the generalized weights of a binary linear code of a given size we also prove some asymptotic results on the distance distribution of binary codes

geometric approach to higher weights the notion of higher or generalized weights of codes is just as natural as that of the classical hamming weight the authors adopt the geometric point of view and always treat the q ary case some results and proofs being new the main goal is to present a clear picture of what is known on the subject

enlargement of calderbank shor steane quantum codes it is shown that a classical error correcting code c n k d which contains its dual c sup spl perp spl sube c and which can be enlarged to c n k k 1 d can be converted into a quantum code of parameters n k k n min d 3d 2 this is a generalization of a previous construction it enables many new codes of good efficiency to be discovered examples based on classical bose chaudhuri hocquenghem bch codes are discussed

concatenated quantum codes constructible in polynomial time efficient decoding and error correction a method for concatenating quantum error correcting codes is presented the method is applicable to a wide class of quantum error correcting codes known as calderbank shor steane css codes as a result codes that achieve a high rate in the shannon theoretic sense and that are decodable in polynomial time are presented the rate is the highest among those known to be achievable by css codes moreover the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range

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

recursive parameter identification algorithm stability analysis via pi sharing pi sharing is introduced as an extension of the application of passivity and hyperstability concepts for discrete time systems providing connections between input output and state space stability notions using tools developed within the pi sharing framework new stability results for the output error class identification algorithm are derived this approach offers a clear interpretation of the role of the spr condition in the work of landau and silveira and its absence in the work of tomizuka and altay

list decoding from erasures bounds and code constructions we consider the problem of list decoding from erasures we establish lower and upper bounds on the rate of a binary linear code that can be list decoded with list size l when up to a fraction p of its symbols are adversarially erased such bounds already exist in the literature albeit under the label of generalized hamming weights and we make their connection to list decoding from erasures explicit our bounds show that in the limit of large l the rate of such a code approaches the capacity 1 p of the erasure channel such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate spl omega spl epsiv sup 2 log 1 spl epsiv that can be efficiently list decoded using lists of size o 1 spl epsiv when an adversarially chosen 1 spl epsiv fraction of symbols are erased for arbitrary spl epsiv 0 this improves previous results in this vein which achieved a rate of spl omega spl epsiv sup 3 log 1 spl epsiv

on the generalized hamming weights of product codes the rth generalized hamming weight of a linear code is the minimum support size of any r dimensional subcode it has been found useful in the studies of cryptography and trellis coding the authors derive several results on expressing the generalized hamming weights of a product code in terms of those of its component codes they also formulate a general conjecture

the second and third generalized hamming weights of hermitian codes in this correspondence we determine the second and third generalized hamming weights of all hermitian codes

on a relaxation of spr condition in parallel mras continuous time case it is shown that the strict positive realness spr condition for asymptotic stability of the continuous time parallel model reference adaptive system mras can be removed provided that the parameter adaption law includes a proportional term and the information matrix is made sufficiently large the present result a continuous time counterpart of an earlier result m tomizuka ibid vol 27 no 4 p 505 6 1982 on the discrete time parallel mras

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

on multiple input multiple output ofdm with index modulation for next generation wireless networks multiple input multiple output orthogonal frequency division multiplexing with index modulation mimo ofdm im is a novel multicarrier transmission technique which has been proposed recently as an alternative to classical mimo ofdm in this scheme ofdm with index modulation ofdm im concept is combined with mimo transmission to take advantage of the benefits of these two techniques in this paper we shed light on the implementation and error performance analysis of the mimo ofdm im scheme for next generation 5g wireless networks maximum likelihood ml near ml simple minimum mean square error mmse and ordered successive interference cancellation osic based mmse detectors of mimo ofdm im are proposed and their theoretical performance is investigated it has been shown via extensive computer simulations that mimo ofdm im scheme provides an interesting tradeoff between error performance and spectral efficiency as well as it achieves considerably better error performance than classical mimo ofdm using different type detectors and under realistic conditions

some good quantum error correcting codes from algebraic geometric codes it is shown that quantum error correction can be achieved by the use of classical binary codes or additive codes over f sub 4 in this correspondence with the help of some algebraic techniques the theory of algebraic geometric codes is used to construct an asymptotically good family of quantum error correcting codes and other classes of good quantum error correcting codes our results are compared with the known best quantum codes

bounds on the minimum support weights the minimum support weight d sub r c of a linear code c over gf q is the minimal size of the support of an r dimensional subcode of c a number of bounds on d sub r c are derived generalizing the plotkin bound and the griesmer bound as well as giving two new existential bounds as the main result it is shown that there exist codes of any given rate r whose ratio d sub rd sub 1 is lower bounded by a number ranging from q sup r 1 q sup r q sup r 1 to r depending on r

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

a new adaptive law for robust adaptation without persistent excitation a new adaptive law motivated by the work of loannou and kokotovic 1983 is proposed for the robust adaptive control of plants with unknown parameters in this adaptive law the output error plays a dual role in the adjustment of the control parameter vector the advantages of using the adaptive law over others proposed in the literature are discussed in the ideal case the adaptive system has bounded solutions in addition the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude the adaptive system is also shown to be robust under bounded external disturbances finally it is shown that by suitably modifying the adaptive law the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant simulation results are presented throughout the paper to complement the theoretical developments

performance analysis of zf and mmse equalizers for mimo systems an in depth study of the high snr regime this paper presents an in depth analysis of the zero forcing zf and minimum mean squared error mmse equalizers applied to wireless multiinput multioutput mimo systems with no fewer receive than transmit antennas in spite of much prior work on this subject we reveal several new and surprising analytical results in terms of output signal to noise ratio snr uncoded error and outage probabilities diversity multiplexing d m gain tradeoff and coding gain contrary to the common perception that zf and mmse are asymptotically equivalent at high snr we show that the output snr of the mmse equalizer conditioned on the channel realization is mmse zf ssrsnr where zf is the output snr of the zf equalizer and that the gap ssrsnr is statistically independent of zf and is a nondecreasing function of input snr furthermore as ssr snr ura ssrsnr converges with probability one to a scaled f random variable it is also shown that at the output of the mmse equalizer the interference to noise ratio inr is tightly upper bounded by ssrsnr zf using the decomposition of the output snr of mmse we can approximate its uncoded error as well as outage probabilities through a numerical integral which accurately reflects the respective snr gains of the mmse equalizer relative to its zf counterpart the e outage capacities of the two equalizers however coincide in the asymptotically high snr regime we also provide the solution to a long standing open problem applying optimal detection ordering does not improve the d m tradeoff of the vertical bell labs layered space time v blast architecture it is shown that optimal ordering yields a snr gain of 10log10n db in the zf v blast architecture where n is the number of transmit antennas whereas for the mmse v blast architecture the snr gain due to ordered detection is even better and significantly so

the weight hierarchy of product codes the weight of a code is the number of coordinate positions where no codeword is zero the rth minimum weight d sub r is the least weight of an r dimensional subcode wei and yang 1993 gave a conjecture about the minimum weights for some product codes in this article we find a relation between product codes and the segre embedding of a pair of projective systems and we use this to prove the conjecture

on the achievable rate of ofdm with index modulation orthogonal frequency division multiplexing with index modulation ofdm im is a recently developed transmission technique that extends the principle of spatial modulation to ofdm subcarriers in this paper the performance of ofdm im is studied in terms of the achievable rate assuming an m ary constellation and that channel state information is available at the receiver a closed form lower bound is derived based on which an interleaved grouping method is proposed for the use of subcarriers in comparison with the existing grouping method the proposed one can better benefit from the diversity effects over frequency selective fading channels especially when the spacing of any two subcarriers within a subcarrier group is larger than the coherence bandwidth through numerical results it is revealed that ofdm im with interleaved grouping outperforms classical ofdm for small m and certain ranges of signal to noise ratio finally the effects of modulation types on the performance of ofdm im are studied it is found that the superiority of ofdm im over classical ofdm is greater for phase shift keying than for quadrature amplitude modulation

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

footprints or generalized bezout s theorem in two previous papers the first by feng rao berg and zhu see ibid vol 43 p 1799 810 1997 and the second by feng zhu shi and rao see proc 35th afferton conf communication control and computing p 205 14 1997 the authors use a generalization of bezout s theorem to estimate the minimum distance and generalized hamming weights for a class of error correcting codes obtained by evaluation of polynomials in points of an algebraic curve the main aim of this article is to show that instead of using this rather complex method the same results and some improvements can be obtained by using the so called footprint from grobner basis theory we also develop the theory further such that the minimum distance and the generalized hamming weights not only can be estimated but also can actually be determined

on binary constructions of quantum codes recently steane 1998 proposed an enlargement of the calderbank shor steane construction here we further improve on the parameters obtained from his construction present examples of new codes and analyze asymptotical non constructive bounds

minimum distance of symplectic grassmann codes abstract in this paper we introduce symplectic grassmann codes in analogy to ordinary grassmann codes and orthogonal grassmann codes as projective codes defined by symplectic grassmannians lagrangian grassmannian codes are a special class of symplectic grassmann codes we describe all the parameters of line symplectic grassmann codes and we provide the full weight enumerator for the lagrangian grassmannian codes of rank 2 and 3

weight distributions of geometric goppa codes the in general hard problem of computing weight distributions of linear codes is considered for the special class of algebraic geometric codes defined by goppa in the early eighties known results restrict to codes from elliptic curves we obtain resullts for curves of higher genus by expressing the weight distributions in terms of l series the results include general properties of weight distributions a method to describe and compute weight distributions and worked out examples for curves of genus two and three

on the weight hierarchy of geometric goppa codes the weight hierarchy of a linear code is the set of generalized hamming weights of the code in the paper the authors consider geometric goppa codes and provide a lower bound on their generalized hamming weights similar to goppa s lower bound on their minimum distance in the particular case of hermitian codes exact results on the second and third generalized hamming weights are given for any m except a few cases where m is a parameter that governs the dimension of these codes in many instances the authors are able to provide considerably more information on their generalized hamming weights an upper bound relating the generalized hamming weights of hermitian codes to the pole numbers at a special point on the curve is also provided similar results are given in the case of codes from some subfields of the hermitian function fields which are also maximal finally a nontrivial family of codes is also presented whose weight hierarchy is completely determined

a new upper bound on the block error probability after decoding over the erasure channel motivated by cryptographic applications we derive a new upper bound on the block error probability after decoding over the erasure channel the bound works for all linear codes and is in terms of the generalized hamming weights it turns out to be quite useful for reed muller codes for which all the generalized hamming weights are known whereas the full weight distribution is only partially known for these codes the error probability is related to the cryptographic notion of algebraic immunity we use our bound to show that the algebraic immunity of a random balanced m variable boolean function is of order m 2 1 o 1 with probability tending to 1 as m goes to infinity

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

on the construction of nonbinary quantum bch codes four quantum code constructions generating several new families of good nonbinary quantum nonprimitive nonnarrow sense bose chaudhuri hocquenghem codes are presented in this paper the first two are based on calderbank shor steane css construction derived from two nonprimitive bose chaudhuri hocquenghem codes the third one is based on steane s enlargement of nonbinary css codes applied to suitable subfamilies of nonprimitive nonnarrow sense bose chaudhuri hocquenghem codes the fourth construction is derived from suitable subfamilies of hermitian dual containing nonprimitive nonnarrow sense bose chaudhuri hocquenghem codes these constructions generate new families of quantum codes whose parameters are better than the ones available in the literature

parallel mras without compensation block the parallel model reference adaptive system mras is shown to be asymptotically stable without the compensation block provided that a quadratic form of the adjustable model input output is lower bounded

adaptive algorithm structure impacts on stability and performance the structures of adaptive algorithms are examined for their impact on input output stability and performance measures three general algorithm structures are considered the a priori form the a posteriori form and the proportional integral pi form a parallel development is used to directly compare continuous and discrete time versions of the algorithms considered the standard a priori and a posteriori algorithm forms are shown to be special cases of a more flexible proportional plus integral algorithm which is implemented via normalization in the adaptive law it is shown that this normalization can enhance algorithm stability and input output performance of normalized errors but the performance unnormalized errors may not be significantly affected this direct comparison of simple algorithm structures serves to isolate the stability and performance properties due to these structures alone it provides information for algorithm design allowing the essential effects of design options to be traded off against the many other options

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

constacyclic codes and some new quantum mds codes one central theme in quantum error correction is to construct quantum codes that have a large minimum distance quantum maximal distance separable mds codes are optimal in the sense they attain maximal minimum distance recently constructing quantum mds codes has received much attention and seems to become more and more difficult in this paper based on classical constacyclic codes we construct some new quantum mds codes by employing the hermitian construction compared with the known quantum mds codes these quantum mds codes have much larger minimum distance

robust adaptive control conditions for global stability an input output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics the concept of a tuned system is introduced i e the control system that could be obtained if the plant were known comparing the adaptive system to the tuned system results in the development of a generic adaptive error system passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller and ensure boundedness of the adaptive gains specific bounds are presented for certain significant signals in the control systems limitations of these global results are discussed particularly the requirement that a certain operator be strictly positive real spr a condition that is unlikely to hold due to unmodeled dynamics

on the weight hierarchy of preparata codes over z sub 4 hammons et al see ibid vol 40 p 301 19 1994 showed that when properly defined the binary nonlinear preparata code can be considered as the gray map of a linear code over z sub 4 the so called preparata code over z sub 4 we consider the rth generalized hamming weight d sub r m of the preparata code of length 2 sup m over z sub 4 for any m spl ges 3 d sub r m is exactly determined for r 0 5 1 1 5 2 2 5 and 3 0 for a composite m we give an upper bound on d sub r m using the lifting technique for m 3 4 5 6 and 8 the weight hierarchy is completely determined in the case of m 7 the weight hierarchy is completely determined except for d sub 4 7

parameter drift in lms adaptive filters we examine general conditions under which the lms adaptive filter generates unbounded parameter estimates when driven by bounded sequences this unexpected parameter divergence or drift is related to the inadequacy of excitation in the input sequence and is characterized by slow i e nonexponential escape of the parameter estimate vector to infinity in spite of all other signals inputs outputs prediction errors remaining bounded or even decaying to zero the analysis proceeds by showing that in a general adaptive filtering setting the sequence of regressors information vectors provides a natural decomposition of the parameter estimate space into subspaces each corresponding to a characteristic class of filter excitation this subspace decomposition is applied to the lms adaptive filter yielding direct links between filter behavior and modes of excitation in particular stability and instability of the parameter estimates in the presence of bounded disturbances and prediction errors is obtained for various classes of excitation this behavior is examined in detail for the first and second order cases and is sufficient to characterize the behavior of higher order adaptive filters the instability drift results are due to modes of decaying excitation and bounds on the rates of drift are derived this drift mechanism is inherent in the algorithm and is not due to numerical implementation problems or violation of small step size conditions examples are presented where drift may occur in restricted complexity filtering and in the related stochastic gradient algorithm an analysis of leakage in terms of input excitation reveals a tradeoff in performance between parameter and prediction errors a modified form of leakage using the subspace decomposition is suggested to remove this difficulty

quantum codes from concatenated algebraic geometric codes we apply steane s enlargement of the calderbank shor steane css codes and additive codes over f sub 4 to concatenated algebraic geometric codes to construct many good quantum codes with fewer restrictions on the parameters compared to some known quantum codes some of the quantum codes we have constructed are either optimal or have parameters as good as the best known codes while some have parameters better than those obtained from other known constructions

on the second relative greedy weight of 4 dimensional codes based on applications to the wire tap channel of type ii with the coset coding scheme we will define optimal codes which are described as the ones achieving upper bounds on e 2 m 2 where e 2 and m 2 are the second relative greedy weight and the second relative generalized hamming weight respectively by using the finite geometry method we will first classify all the 4 dimensional codes with respect to their k 1 dimensional subcodes for k 1 1 and k 1 2 and determine the upper bounds on e 2 m 2 for each class of codes and then obtain optimal codes by explicitly constructing the value assignments which achieve upper bounds on e 2 m 2

codes satisfying the chain condition the authors considered weight hierarchies of codes satisfying the chain condition they called these chain good first they gave a set of simple necessary conditions for a sequence to be chain good they proved that given one chain good sequence there is an infinite set of chain good sequences that can be constructed from this one sequence finally they used this result to completely describe the sets of chain good sequences of dimensions up to 5

application of constacyclic codes to quantum mds codes quantum maximum distance separable mds codes form an important class of quantum codes to get q ary quantum mds codes one of the effective ways is to find linear mds codes c over f q2 satisfying c h c where c h denotes the hermitian dual code of c for a linear code c of length n over f q2 we say that c is a dual containing code if c h c and c f q2 n several classes of new quantum mds codes with relatively large minimum distance have been produced through dual containing constacyclic mds codes these works motivate us to make a careful study on the existence conditions for dual containing constacyclic codes we obtain necessary and sufficient conditions for the existence of dual containing constacyclic codes four classes of dual containing constacyclic mds codes are constructed and their parameters are computed consequently the quantum mds codes are derived from these parameters the quantum mds codes exhibited here have minimum distance bigger than the ones available in the literature

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

disturbance instabilities in an adaptive system two types of disturbance instability of simple adaptive schemes are analyzed a drift equation shows how stable equilibria are forced to infinity by infrequent but persistent switches of a constant disturbance the modification proposed by p ioannou counteracts these instabilities

space time block coded spatial modulation a novel multiple input multiple output mimo transmission scheme called space time block coded spatial modulation stbc sm is proposed it combines spatial modulation sm and space time block coding stbc to take advantage of the benefits of both while avoiding their drawbacks in the stbc sm scheme the transmitted information symbols are expanded not only to the space and time domains but also to the spatial antenna domain which corresponds to the on off status of the transmit antennas available at the space domain and therefore both core stbc and antenna indices carry information a general technique is presented for the design of the stbc sm scheme for any number of transmit antennas besides the high spectral efficiency advantage provided by the antenna domain the proposed scheme is also optimized by deriving its diversity and coding gains to exploit the diversity advantage of stbc a low complexity maximum likelihood ml decoder is given for the new scheme which profits from the orthogonality of the core stbc the performance advantages of the stbc sm over simple sm and over v blast are shown by simulation results for various spectral efficiencies and are supported by the derivation of a closed form expression for the union bound on the bit error probability

code construction for the noiseless binary switching multiple access channel the noiseless coding problem is considered for a discrete memoryless multiple access channel that is a counterpart to the well known binary adder channel upper and lower bounds on the number of code words in a uniquely decodable code pair are given from which the zero error capacity region of the channel is derived this region coincides with the classical capacity region of this channel the proof uses the notion of second order distance of a code for several values of n and k good code pairs of block length n are constructed with the first code being n k linear some of these are found to be optimal some convolutional codes are investigated that yield additional good rate pairs

dominant richness and improvement of performance of robust adaptive control abstract several recent robust adaptive control schemes guarantee stability and residual tracking errors which are small in the mean for any bounded initial conditions independent of any persistence of excitation condition since smallness in the mean does not always guarantee small bounds for the tracking error at steady state the tracking performance of these robust schemes may not be acceptable in this paper we show that the convergence and the tracking performance of these globally stable adaptive control schemes can be considerably improved if the reference input signal is chosen to be dominantly rich we show that dominantly rich signals maintain a high level of persistence of excitation relative to the level of the modeling error which guarantees exponential convergence and small bounds for the tracking and parameter error at steady state

minimum support weights of binary codes some relations between the minimum support weights are discussed in particular the possible weight hierarchies of codes of dimension 4 are determined

a systolic array implementation of the feng rao algorithm an efficient implementation of a parallel version of the feng rao algorithm on a one dimensional systolic array is presented in this paper by adopting an extended syndrome matrix syndromes of the same order lying on a slant diagonal in the extended syndrome matrix are scheduled to be examined by a series of cells simultaneously and therefore a high degree of concurrency of the feng rao algorithm can be achieved the time complexity of the proposed architecture is m g 1 by using a series of t g 1 2 1 nonhomogeneous but regular effective processors called pe cells and g trivial processors called d cells where t is designed as the half of the feng rao bound each d cell contains only delay units while each pe cell contains one finite field inverter and except the first one one or more finite field multipliers cell functions of each pe cell are basically the same and the overall control circuit of the proposed array is quite simple the proposed architecture requires in total t g 1 1 finite field inverters and t g 1 2 t g 1 2 1 2 finite field multipliers for a practical design this hardware complexity is acceptable

orthogonal frequency division multiplexing with index modulation in this paper a novel orthogonal frequency division multiplexing ofdm scheme called ofdm with index modulation ofdm im is proposed for operation over frequency selective and rapidly time varying fading channels in this scheme the information is conveyed not only by m ary signal constellations as in classical ofdm but also by the indices of the subcarriers which are activated according to the incoming bit stream different low complexity transceiver structures based on maximum likelihood detection or log likelihood ratio calculation are proposed and a theoretical error performance analysis is provided for the new scheme operating under ideal channel conditions then the proposed scheme is adapted to realistic channel conditions such as imperfect channel state information and very high mobility cases by modifying the receiver structure the approximate pairwise error probability of ofdm im is derived under channel estimation errors for the mobility case several interference unaware aware detection methods are proposed for the new scheme it is shown via computer simulations that the proposed scheme achieves significantly better error performance than classical ofdm due to the information bits carried by the indices of ofdm subcarriers under both ideal and realistic channel conditions

further results on the semilinear equivalence of linear codes based on relative subcodes we address an equivalent condition for a one to one semilinear mapping between two linear codes to be in fact a semimonomial transformation that is the underlying two codes are semilinearly equivalent the result in the present paper substantially improves the equivalent condition in recent literatures moreover it also generalizes the well known macwilliams theorem of code equivalence

generalized macwilliams identities for spl zopf sub 4 linear codes in this correspondence the generalized macwilliams identities between the support weight distributions of a spl zopf sub 4 linear code of type 4 sup k and that of its dual are established