on group theoretic codes for asymmetric channels we study single error correcting codes for the asymmetric channel with input and output alphabets being 0 1 a 1 from an abelian group g of order n with elements g0 0 g1 gn 1 constantin and rao 1979 inform contr 40 20 36 define vg b1 b2 bn 1 o 1 a 1 n 1 n 1i 1 bigi 0 g and show that vg correct single errors we give explicit expressions for the size and weight distribution of these codes we further give a short discussion of some constant weight codes obtained by a similar construction

moment balancing templates for d k constrained codes and run length limited sequences the first order moment of d k constrained codes is investigated in this paper a generalized moment balancing template is proposed to encode a d k sequence into a single insertion or deletion correcting codeword without losing the constraint property by relocating 0 s in moment balancing runs which appear in a pairwise manner of a d k sequence the first order moment of this sequence can be modified to satisfy the varshamov tenengolts construction with a reasonably large base in the modulo system introduced by the varshamov tenengolts construction this generalized moment balancing template can be applied to run length limited sequences the asymptotic bound of the redundancy introduced by the template for d k sequences is of the same order as the universal template for random sequences and therefore the redundancy is small and suitable for long sequences of practical interest

paraxial space domain formulation for surface fields on a large dielectric coated circular cylinder a new method to evaluate the surface fields excited within the paraxial nearly axial region of an electrically large dielectric coated circular cylinder is presented this representation is obtained by performing the watson s transformation in the standard eigenfunction solution and using the fact that the circumferentially propagating series representation of the appropriate green s function is periodic in one of its two variables therefore it can be approximated by a fourier series where the two leading terms of the expansion yield engineering accuracy in most cases this work can be used in conjunction with a method of moments solution for the design analysis of conformal microstrip antennas and arrays numerical results are presented and compared with a standard eigenfunction expansion

scattering from a cylindrically conformal slotted waveguide array antenna a numerical method is developed to investigate electromagnetic scattering by a cylindrically conformal waveguide fed slot array the problem is first formulated in terms of integral equations using the equivalence principle the integral equations are then solved using the method of moments mom in conjunction with global sinusoidal basis functions and galerkin s testing procedure the mom solution requires the evaluation of the generalized admittance matrices involving various dyadic green s functions the slow convergence of the series associated with the summation of waveguide modes is accelerated using the kummer transformation and the slow convergence of the series associated with the summation of the exterior modes is avoided by using the asymptotic solutions with proper treatment for singular integrals the evaluation of the excitation vector and scattered field is also accelerated using watson s transformation and asymptotic solutions numerical results are presented to illustrate the scattering characteristics of the cylindrically conformal waveguide fed slot arrays such as the effects of curvature slot thickness and waveguide termination on the radar cross section rcs of the arrays

invariance groups of transformations of basic hypergeometric series we show that certain two term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups for the transformations of nonterminating 3 2 series and those of terminating balanced 4 3 series these invariance groups are symmetric groups for transformations of 2 1 series the invariance group is the dihedral group of order 12 transformations of terminating 3 2 series are described by means of some subgroup of s6 and finally the invariance group of transformations of very well poised nonterminating 8 7 series is shown to be isomorphic to the weyl group of a root system of type d5

scattering by cavity backed antennas on a circular cylinder conformal arrays are popular antennas for aircraft spacecraft and land vehicle platforms due to their inherent low weight drag and observables however to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer in fact it has been common practice to use limited measurements and planar approximations in designing such nonplanar antennas we extend the finite element boundary integral method to scattering by cavity backed structures in an infinite metallic cylinder in particular we discuss the formulation specifics such as weight functions dyadic green s function implementation details and particular difficulties inherent to cylindrical structures special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements scattering results are presented and validated as much as possible

lee metric bch codes and their application to constrained and partial response channels shows that each code in a certain class of bch codes over gf p specified by a code length n spl les p sup m 1 and a runlength r spl les p 1 2 of consecutive roots in gf p sup m has minimum lee distance spl ges 2r for the very high rate range these codes approach the sphere packing bound on the minimum lee distance furthermore for a given r the length range of these codes is twice as large as that attainable by berlekamp s 1984 extended negacyclic codes the authors present an efficient decoding procedure based on euclid s algorithm for correcting up to r 1 errors and detecting r errors that is up to the number of lee errors guaranteed by the designed minimum lee distance 2r bounds on the minimum lee distance for r spl ges p 1 2 are provided for the reed solomon case i e when the bch code roots are in gf p the authors present two applications first lee metric bch codes can be used for protecting against bitshift errors and synchronization errors caused by insertion and or deletion of zeros in d k constrained channels second the code construction with its decoding algorithm can be formulated over the integer ring providing an algebraic approach to correcting errors in partial response channels where matched spectral null codes are used

mutual admittance between slots in cylinders of arbitrary shape a numerical formulation involving the fourier transform and the combined field integral equation is presented to calculate the mutual admittance between axial slots or circumferential slots in arbitrarily shaped cylinders two cases are considered coupling between two circumferential slots and coupling between two axial slots the slots are assumed to be waveguide fed apertures excited with the te sub 10 waveguide mode with no higher order modes included in the model the combined field integral equation cfie formulation was used in conjunction with the magnetic field integral equation mfie to solve the resulting two dimensional integral equation formulations for the axial slot case are discussed results concerning the discretization and truncation of the spectrum as well as the accuracy of the procedure are presented for both axial and circumferential cases the accuracy of the procedure is demonstrated by comparison with eigenfunction data for circular cylinders

generalized zernike or disc polynomials an application in quantum optics an application of the generalized zernike or disc polynomials recently introduced in the literature is shown resorting to the lie algebra based investigation of the dynamics of quantum systems driven by two mode interaction hamiltonians further properties of the associated disc functions are deduced also a generalization of the disc polynomials towards the hahn polynomials is suggested

analysis of printed antennas mounted on a coated circular cylinder of arbitrary size an efficient numerical algorithm for the analysis of printed antennas on a dielectric coated circular cylinder is presented the formulation employs the spectral domain approach green s function is evaluated via olver s uniform asymptotic expansions the fourier summation is transformed into integration and the asymptotic part of the integral is evaluated in closed form the whole procedure results in a numerical algorithm that is at least as accurate and efficient as the respective one for the planar structure the present approach can be applied for any source receiver position and any cylinder radius

reducing the backscattering via complex impedance coating a method for reducing the back scattering from bodies with complex impedance boundaries is developed a nonlinear integral equation system providing zero backscattering is obtained for determining the impedance distribution on the boundaries of infinite cylinders numerical results for circular and elliptic cylinders are given frequency dependence of backscattering at obtained optimal impedance is discussed on the example of circular cylinder

an asymptotic solution for the surface magnetic field within the paraxial region of a circular cylinder with an impedance boundary condition it is well known that the high frequency asymptotic evaluation of surface fields by the conventional geometrical theory of diffraction gtd usually becomes less accurate within the paraxial close to axial region of a source excited electrically large circular cylinder uniform versions of the gtd based solution for the surface field on a source excited perfect electrically conducting pec circular cylinder were published earlier to yield better accuracy within the paraxial region of the cylinder however efficient and sufficiently accurate solutions are needed for the surface field within the paraxial region of a source excited circular cylinder with an impedance boundary condition ibc in this work an alternative approximate asymptotic closed form solution is proposed for the accurate representation of the tangential surface magnetic field within the paraxial region of a tangential magnetic current excited circular cylinder with an ibc similar to the treatment for the pec case hankel functions are asymptotically approximated by a two term debye expansion within the spectral integral representation of the relevant green s function pertaining to the ibc case although one of the two integrals within the spectral representation is evaluated in an exact fashion the other integral for which an exact analytical evaluation does not appear to be possible is evaluated asymptotically unlike the pec case in which both integrals were evaluated analytically in an exact fashion validity of the proposed asymptotic solution is investigated by comparison with the exact eigenfunction solution for the surface magnetic field

efficient computation of nonparaxial surface fields excited on an electrically large circular cylinder with an impedance boundary condition an alternative numerical approach is presented for the evaluation of the fock type integrals that exist in the uniform geometrical theory of diffraction utd based asymptotic solution for the nonparaxial surface fields excited by a magnetic or an electric source located on the surface of an electrically large circular cylinder with an impedance boundary condition ibc this alternative approach is based on performing numerical integration of the fock type integrals on a deformed path on which the integrands are nonoscillatory and rapidly decaying comparison of this approach with the previously developed one presented in which is based on invoking the cauchy s residue theorem by finding the pole singularities numerically reveals that the alternative approach is considerably more efficient

efficient computation of surface fields excited on a dielectric coated circular cylinder an efficient method to evaluate the surface fields excited on an electrically large dielectric coated circular cylinder is presented the efficiency of the method results from the circumferentially propagating representation of the green s function as well as its efficient numerical evaluation along a steepest descent path the circumferentially propagating series representation of the appropriate green s function is obtained from its radially propagating counterpart via watson s transformation and then the path of integration is deformed to the steepest descent path on which the integrand decays most rapidly numerical results are presented that indicate that the representations obtained here are very efficient and valid even for arbitrary small separations of the source and field points this work is especially useful in the moment method analysis of conformal microstrip antennas where the mutual coupling effects are important

evaluation of hankel functions with complex argument and complex order the use of f w j olver s 1974 uniform asymptotic expansions to compute hankel functions of interest in em scattering of complex argument z and complex order v is examined emphasis is placed on how to choose the proper branches in evaluation of the complex functions in the asymptotic representations comparison is made with the nonuniform formulas of debye and watson the debye formulas are valid when z and v are far apart and the watson formulas are valid when z and v are close together the fact that the olver formulas are uniform is important from a numerical viewpoint because a satisfactory criterion for deciding when to switch between the debye and watson 1958 formulas is not available validation by comparison with two nonasymptotic methods verifies that the olver formulas are considerably more accurate than the debye or watson formulas

codes correcting a single insertion deletion of a zero or a single peak shift codes of d k sequences of constant hamming weight are considered perfect codes correcting a single insertion deletion or peak shift are defined and shown to exist a systematic method to construct large classes of perfect codes is given a number of related problems are considered

a scheme for automatic computation of fock type integrals the evaluation of fock type integrals i e integrals that are formally the fourier transform of a slowly varying factor comprising a quotient of terms containing airy functions and their derivatives is developed in a computationally efficient way the integrals are evaluated by use of a simple extension of a fourier quadrature method that is related to the discrete fourier transform the resulting quadrature is applicable to both surface field and reflected field fock integrals for a lossy impedance surface the computation is believed to be efficient enough to allow the use of these functions in field computations codes where the fock integrals must be computed on an as needed basis

using reed muller hbox rm 1 m codes over channels with synchronization and substitution errors we analyze the performance of a reed muller rm 1 m code over a channel that in addition to substitution errors permits either the repetition of a single bit or the deletion of a single bit the latter feature is used to model synchronization errors we first analyze the run length structure of this code we enumerate all pairs of codewords that can result in the same sequence after the deletion of a single bit and propose a simple way to prune the code by dropping one information bit such that the resulting linear subcode has good post deletion and post repetition minimum distance a bounded distance decoding algorithm is provided for the use of this pruned code over the channel this algorithm has the same order of complexity as the usual fast hadamard transform based decoder for the rm 1 m code

phased arrays of rectangular apertures on conformal cylindrical surfaces a multimode equivalent network approach in this paper we present an efficient integral equation formulation based on a multimode equivalent network men approach for the analysis of phased arrays on cylindrical surfaces using open ended waveguide radiators in addition to theory experimental data are also presented showing very good agreement with simulated results

generalized basic hypergeometric functions and the q analogues of 3 j and 6 j coefficients the racah wigner algebra for the quantum group suq 2 is developed to derive explicit expressions for the q analogues of the van der waerden racah wigner and majumdar forms of the 3 j coefficient given in terms of sets of basic hypergeometric functions interrelationships between the members of a given set of 3 phi 2 are established using the reversal of series or the q to q 1 operation starting with the van der waerden set using three transformations of 3 phi 2s 12 other sets including the racah wigner and majumdar sets have been obtained in the simpler case of the q analogue of the 6 j coefficients two sets of 4 phi 3s related to each other by reversal of series are obtained

an asymptotic solution for surface fields on a dielectric coated circular cylinder with an effective impedance boundary condition an effective surface impedance approach is introduced for determining surface fields on an electrically large dielectric coated metallic circular cylinder differences in analysis of rigorously treated coated metallic cylinders and cylinders with an impedance boundary condition ibc are discussed while for the impedance cylinder case a single constant surface impedance is considered for the coated metallic cylinder case two surface impedances are derived these are associated with the tm and te creeping wave modes excited on a cylinder and depend on observation and source positions and orientations with this in mind a uniform theory of diffraction utd based method with ibc is derived for the surface fields by taking into account the surface impedance variation the asymptotic expansion is performed via the watson transformation over the appropriate series representation of the green s functions thus avoiding higher order derivatives of fock type integrals and yielding a fast and an accurate solution numerical examples reveal a very good accuracy for large cylinders when the separation between the observation and the source point is large thus this solution could be efficiently applied in mutual coupling analysis along with the method of moments mom of large conformal microstrip array antennas

classification of the deletion correcting capabilities of reed solomon codes of dimension 2 over prime fields deletion correction codes have been used for transmission synchronization and more recently tracing pirated media a generalized reed solomon grs code denoted by grsk l q alpha v is a code of length l over gf q with qk codewords these codes have an efficient decoding algorithm and have been widely used for error correction and detection it was recently demonstrated that grs codes are also capable of correcting deletions we consider a subclass of grs codes with dimension k 2 and q prime and study them with respect to deletion correcting capability we give transformations that either preserve the code or maintain its deletion correction capability we use this to define equivalent codes and then use exhaustive and selective computer searches to find inequivalent codes with the highest deletion correcting capabilities we show that for the class under consideration up to l 3 deletions may be corrected we also show that for lles36 there exist codes with q2 codewords such that receiving only 3 out of t transmitted symbols of a codeword is enough to recover the codeword thus meeting the bound specified above we also specify some nice codes which are associated with the smallest field possible for codes of a given length and deletion correcting capability some of the identified codes are unique with respect to the defined equivalence

four sets of 3f2 1 functions hahn polynomials and recurrence relations for the 3 j coefficients the wigner racah and majumdar sets of 3f2 1 are derived from the symmetric van der waerden set of 3f2 1 for the 3 j coefficient using a transformation due to erdelyi and weber 1952 which is also used to relate the 3 j coefficient to a discrete orthogonal hahn polynomial the four recurrence relations one old and three new obtained by karlin and mcgregor 1961 for the hahn polynomial are used to derive recurrence relations for the 3 j coefficient two of which have been shown to be useful in the exact recursive evaluation of the 3 j coefficients by schulten and gordon

group theoretical basis for the terminating 3f2 1 series it is shown that a recursive use of the transformation for a terminating 3f2 1 series used by weber and erdelyi 1952 which belongs as shown by whipple 1925 to a set of equivalent 3f2 1 functions obtained by thomae 1979 results in a 72 element group associated with 18 terminating series the generators conjugacy classes invariant subgroups characters and dimensions of irreducible representations for this group are presented

perfect d k codes capable of correcting single peak shifts codes for the multibit peak shift recording channel called d k codes of reduced length n are considered arbitrary d k and perfect d k codes capable of correcting single peak shifts of given size t are defined for the construction of perfect codes a general combinatorial method connected with finding good weight sequences in abelian groups is used and the concept of perfect t shift n designs is introduced explicit constructions of such designs for t 1 t 2 and t p 1 2 are given where p is a prime this construction is universal in that it does not depend on the d k constraints it also allows automatic correction of those peak shifts that violate d k constraints the construction is extended to d k codes of fixed binary length and allows the beginning of the next codeword to be determined the question whether the designed codes can be represented as systematic codes with minimal redundancy is considered as well

hybrid finite element boundary integral method for cavities recessed in an elliptic cylinder the highly versatile finite element boundary integral method is presented for accurate modeling of fields within cavities recessed in a perfectly conducting infinite elliptic cylinder properties of flush mounted cavities and antennas are explored and compared with prior developments this formulation represents a significant advancement over prior techniques since surface curvature variation either across a single element or across an array of elements is now accurately included into the antenna model an advantage of this approach is the ability to model cavities with curvature varying from planar to the constant curvature of a circular cylinder computed eigenvalues for planar rectangular and cylindrical rectangular closed cavities are compared with theoretical values eigenvalues are presented for elliptic rectangular cavities furthermore the input impedance of a conformal cavity backed patch antenna mounted on an elliptic cylinder is presented and compared with a similar antenna on a circular cylinder

a new look at azimuthal wave propagation constants of an n layered dielectric coated pec cylinder a method for determining the azimuthal wave propagation constants supported by an n layered dielectric coated pec cylinder is presented the method based on a green s function described in is designed to optimally handle layered cylinders where the number of layers is extremely large as might be encountered in structures designed using transformational optics the method is also tractable for any stratification profile without the need for individual layer analysis we implement a recently developed numerical method to calculate bessel functions of complex order and argument our method is verified by comparison with previously published results we also present new results for a 5 layer case demonstrating self consistency and improved accuracy over published methods finally to illustrate the method s benefits we present a brief analysis of two multilayer structures a multilayer variation of the coated cylinder presented in and an example of a 7 layer case that approximates a material parameter gradient

analysis and measurements of conformal patch array antennas on multilayer circular cylinder in this paper we present a method of moments mom program to analyze different configurations of arrays of cylindrical rectangular patches the patches can be located inside or on the surface of a multilayer circular cylindrical structure and can be arbitrarily rotated the antenna structure is rigorously taken into account by using proper green s functions and the array is analyzed by using an element by element approach the elements of the mom matrix are calculated in the spectral domain and special attention is given to their numerical treatment when analyzing cylindrical antennas with large radii a laboratory model is built to test different configurations of patches and to validate calculated results the agreement between measurements and calculations is very good

admittance of rectangular waveguide radiating from a conducting cylinder theory and experiment are compared for the admittance presented to a rectangular waveguide which terminates at an arbitrary angle in the surface of a conducting cylinder two methods are described for calculating the admittance a single mode approximation from the modal solution and an alternative asymptotic solution using these methods the effect of aperture orientation on admittance and the results obtained are compared with the experiment the single mode approximation is in good agreement with experimental results for the case when the input waveguide supports the te sub 10 mode only the accuracy of the approximate formula for waveguide admittance was also verified the admittance is shown to be weakly dependent on aperture orientation for moderately large cylinders

accurate asymptotic solution for the surface field due to apertures in a conducting cylinder asymptotic solutions for the surface field due to a magnetic point source on a cylinder can simplify the computational task in the analysis of mutual coupling e g in conformal arrays although several asymptotic solutions are at present available their accuracy is limited the aim here is to obtain a new approximate solution with improved accuracy an asymptotic solution of the exact modal solution for the field on a cylinder which contains terms up to k 0 t 2 where t is the distance from the source is derived approximate terms up to k 0 t 3 are included from the solution for a source on a plane conductor and an earlier asymptotic solution the new approximate solution consists of the exact solution for a plane conductor modulated by a fock function plus a contribution associated with the cylinder which vanishes in the limit of infinite radius typically for cylinders of radius greater than one and half wavelengths it agrees to within 0 5 db in magnitude and 1 deg in phase of the modal solution results for dominant mode mutual and self admittances of rectangular apertures on a cylinder obtained from this solution are presented a formula is also given for calculating self admittances from an asymptotic solution there is excellent agreement between admittances computed from the asymptotic solution and the modal solution one exception is the self susceptance of an axial slot where the error is larger than expected although the error is low enough to be acceptable in most practical cases

uniform asymptotic solution for the surface magnetic field valid both within and outside the paraxial region of a perfect electrically conducting circular cylinder high frequency methods employed for the perfect electrically conducting circular cylinder form two sets the uniform theory of diffraction utd based ones are valid outside the paraxial region while there are others that are accurate close to the axis of the cylinder here we present a uniform asymptotic solution for the surface magnetic field valid both within and outside the paraxial region of a perfect electrically conducting circular cylinder this is achieved by approximating the hankel functions by a uniform asymptotic expansion within the spectral integral representation of the relevant green s function all the resulted integrals are evaluated analytically in an exact fashion such a solution is of interest both for theoretical and for practical reasons from a theoretical point of view it is important to have a closed form solution that copes with the canonical problem of a perfect electrically conducting circular cylinder from a practical point of view such a solution provides mutual coupling results and thus predicts compatibility and interference between conformal slot antennas mounted on constant radius cylindrically shaped perfectly conducting hosts validity of the proposed asymptotic solution is provided by comparison with published results

a lower bound for a n 4 w corresp an explicit lower bound is given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance four and constant weight w

asymptotically good codes correcting insertions deletions and transpositions we present simple polynomial time encodable and decodable codes which are asymptotically good for channels allowing insertions deletions and transpositions as a corollary they achieve exponential error probability in a stochastic model of insertion deletion