simple discontinuities in acoustic waveguides at low frequencies critical analysis and formulae the variational method of schwinger is applied to reach qualitative conclusions regarding the effects of symmetrical discontinuities change in cross section diaphragm of zero thickness in acoustic waveguides for bidimensional geometry the exact results from an analytical solution are used to discuss the convergence of the solutions of the modal theory when the number of modes taken into account increases the variation of the discontinuity inductances with frequency and the difference between radiation into infinite space and into a large waveguide are discussed finally by a fitting procedure a set of formulae is provided for the engineer for both the case of the radiation of a plane piston into an infinite waveguide and the case of a change in cross section in a circular guide

bicylindrical model of herschel quincke tube duct system theory and comparison with experiment and finite element method an analytical three dimensional bicylindrical model is developed in order to take into account the effects of the saddle shaped area for the interface of a n herschel quincke tube system with the main duct results for the scattering matrix of this system deduced from this model are compared in the plane wave frequency domain versus experimental and numerical data and a one dimensional model with and without tube length correction the results are performed with a two herschel quincke tube configuration having the same diameter as the main duct in spite of strong assumptions on the acoustic continuity conditions at the interfaces this model is shown to improve the nonperiodic amplitude variations and the frequency localization of the minima of the transmission and reflection coefficients with respect to one dimensional model with length correction and a three dimensional model

all the stabilizer codes of distance 3 we give necessary and sufficient conditions for the existence of stabilizer codes n k 3 of distance 3 for qubits n k log2 3n 1 n where n 1 if n 84m 1 3 1 2 or n 4m 2 1 3 1 2 3 for some integer m 1 and n 0 otherwise or equivalently a code n n r 3 exists if and only if n 4r 1 3 4r 1 3 n 1 2 3 for even r and n 8 4r 3 1 3 8 4 3 1 3 n 1 for odd r given an arbitrary length n we present an explicit construction for an optimal quantum stabilizer code of distance 3 that saturates the above bound

sparse quantum codes from quantum circuits we describe a general method for turning quantum circuits into sparse quantum subsystem codes the idea is to turn each circuit element into a set of low weight gauge generators that enforce the input output relations of that circuit element using this prescription we can map an arbitrary stabilizer code into a new subsystem code with the same distance and number of encoded qubits but where all the generators have constant weight at the cost of adding some ancilla qubits with an additional overhead of ancilla qubits the new code can also be made spatially local applying our construction to certain concatenated stabilizer codes yields families of subsystem codes with constant weight generators and with minimum distance d n 1 epsilon where epsilon o 1 sqrt log n for spatially local codes in d dimensions we nearly saturate a bound due to bravyi and terhal and achieve d n 1 epsilon 1 d previously the best code distance achievable with constant weight generators in any dimension due to freedman meyer and luo was o sqrt n log n for a stabilizer code

some new classes of quantum mds codes from constacyclic codes quantum maximum distance separable mds codes form an important family of quantum codes in this paper using hermitian construction and classical constacyclic codes we construct six classes of quantum mds codes two of these six classes of quantum mds codes have larger minimum distance than the ones available in the literature most of these quantum mds codes are new in the sense that their parameters are not covered by the codes available in the literature

binary construction of quantum codes of minimum distance three and four we give elementary recursive constructions of binary self orthogonal codes with dual distance four for all even lengths n spl ges 12 and n 8 consequently good quantum codes of minimum distance three and four for such length n are obtained via steane s construction and the css construction previously such quantum codes were explicitly constructed only for a sparse set of lengths almost all of our quantum codes of minimum distance three are optimal or near optimal and some of our minimum distance four quantum codes are better than or comparable with those known before

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

boolean functions projection operators and quantum error correcting codes this paper describes a fundamental correspondence between boolean functions and projection operators in hilbert space the correspondence is widely applicable and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes the new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original 5 6 2 code found by rains it also extends to operator quantum error correcting codes

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

acoustic length correction of closed cylindrical side branched tube a numerical approach based on the three dimensional boundary element method bem is developed to determine the acoustic length correction of closed cylindrical side branched tube mounted perpendicular to a cylindrical main pipe the effects of helmholtz number and finite length of side branched tube on the acoustic length correction are examined and a curve fitting expression is provided for the acoustically long side branched tube for a pipe mounted concentric helmholtz resonator the transmission loss and resonance frequency are predicted by using the 3 d bem and the corrected 1 d analytical approach to assess the accuracy and applicability of the latter as well as to illustrate the importance of acoustic length correction for an accurate prediction of resonance frequency of the pipe mounted resonator

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

a novel subgridding scheme based on a combination of the finite element and finite difference time domain methods a simple and versatile local mesh refinement scheme based on the hybridization of the finite element fe and the finite difference time domain fdtd algorithms is presented the scheme achieves considerable flexibility in subgridding by using a transition region between the coarse and fine fdtd grids meshed according to an unstructured grid and solved by means of the fe method in the td an interpolation scheme in the time domain which allows the use of different time steps in the coarse and fine mesh regions is included in the paper

quantum reed muller codes a set of quantum error correcting codes based on classical reed muller codes is described the codes have parameters n k d 2 sup r s sup r c r t 2 spl sigma sub i 0 sup t 1 c r i 2 sup t 2 sup t 1

fdtd local grid with material traverse often a finite difference time domain fdtd calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space by locally applying finer grids local grids to these volumes the necessary resolution can be obtained computation time and memory requirements may be far less than for an fdtd space with the smaller mesh resolution throughout in many situations it is important that these local grids function when materials traverse the main grid local grid mg lg boundary surfaces since the volumes that require local grids may not be isolated in a homogeneous medium a local grid method which allows dielectric and or conducting materials to traverse the boundaries is developed three different fdtd problems that utilize the local grid method are used as validation tests results are compared with uniform mesh fdtd solutions

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

asymmetric quantum codes constructions bounds and performance recently quantum error correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit and phase flip errors an example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel where the probabilities of bit and phase flips can be related to relaxation and dephasing time respectively we study asymmetric quantum codes that are obtained from the calderbank shor steane css construction for such codes we derive upper bounds on the code parameters using linear programming a central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes for instance we derive asymmetric codes using a combination of bose chaudhuri hocquenghem bch and finite geometry low density parity check ldpc codes we show that the asymmetric quantum codes offer two advantages namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates our approach is based on a css construction that combines bch and finite geometry ldpc codes

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

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

pseudo cyclic codes and the construction of quantum mds codes constacyclic codes which generalize the classical cyclic codes have played important roles in recent constructions of many new quantum maximum distance separable mds codes however the mathematical mechanism may not have been fully understood in this paper we use pseudo cyclic codes which is a further generalization of constacyclic codes to construct the quantum mds codes we can not only provide a unified explanation of many previous constructions but also produce some new quantum mds codes

application of classical hermitian self orthogonal mds codes to quantum mds codes in this paper we first construct several classes of classical hermitian self orthogonal maximum distance separable mds codes through these classical codes we are able to obtain various quantum mds codes it turns out that many of our quantum codes are new in the sense that the parameters of our quantum codes cannot be obtained from all previous constructions

tables of curves with many points these tables record results on curves with many points over finite fields for relatively small genus 0 g 50 and q a small power of 2 or 3 we give in two tables the best presently known bounds for n q g the maximum number of rational points on a smooth absolutely irreducible projective curve of genus g over a field f q of cardinality q in additional tables we list for a given pair g q the type of construction of the best curve so far and we give a reference to the literature where such a curve can be found

on optimal constacyclic codes abstract in this paper we construct new families of maximum distance separable mds convolutional codes derived from classical constacyclic codes additionally we also construct new families of almost mds block and convolutional codes most of the new convolutional codes constructed here are unit memory and have degree 2 moreover based on a different method we construct families of asymmetric quantum codes known in the literature all these results are mainly derived from the investigation of suitable properties on cyclotomic cosets of such codes

a construction of new quantum mds codes it has been a great challenge to construct new quantum maximum distance separable mds codes in particular it is very hard to construct the quantum mds codes with relatively large minimum distance so far except for some sparse lengths all known q ary quantum mds codes have minimum distance q 2 1 in this paper we provide a construction of the quantum mds codes with minimum distance q 2 1 in particular we show the existence of the q ary quantum mds codes with length n q2 1 and minimum distance d for any d q 1 this result extends those given in the works of guardia 2011 jin et al 2010 and kai an zhu 2012 and with length q2 2 3 and minimum distance d for any d 2q 2 3 if 3 q 1 our method is through hermitian selforthogonal codes the main idea of constructing the hermitian self orthogonal codes is based on the solvability in fq of a system of homogenous equations over fq2

a nonadditive quantum code every good quantum error correcting code discovered thus far such as those known as stabilizer or additive codes has had the structure of an eigenspace of an abelian group generated by tensor products of pauli matrices in this letter we present the first example of a code that is better than any code of this type it encodes six states in five qubits and can correct the erasure of any single qubit

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

quantum codes of minimum distance two it is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2 thus it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize with this in mind we present a number of results on codes of minimum distance 2 we first compute the linear programming bound on the dimension of such a code then show that this bound can only be attained when the code either is of even length or is of length 3 or 5 we next consider questions of uniqueness showing that the optimal code of length 2 or 1 is unique implying that the well known one qubit in five single error correcting code is unique and presenting nonadditive optimal codes of all greater even lengths finally we compute the full automorphism group of the more important distance 2 codes allowing us to determine the full automorphism group of any gf 4 linear code

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

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

sparse graph codes for quantum error correction sparse graph codes appropriate for use in quantum error correction are presented quantum error correcting codes based on sparse graphs are of interest for three reasons first the best codes currently known for classical channels are based on sparse graphs second sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small a constant number per quantum bit independent of the block length third sparse graph codes often offer great flexibility with respect to block length and rate we believe some of the codes we present are unsurpassed by previously published quantum error correcting codes

on quantum and classical bch codes classical bose chaudhuri hocquenghem bch codes that contain their euclidean or hermitian dual codes can be used to construct quantum stabilizer codes this correspondence studies the properties of such codes it is shown that a bch code of length n can contain its dual code only if its designed distance delta o radicn and the converse is proved in the case of narrow sense codes furthermore the dimension of narrow sense bch codes with small design distance is completely determined and consequently the bounds on their minimum distance are improved these results make it possible to determine the parameters of quantum bch codes in terms of their design parameters

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

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