conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

on the dimension of subfield subcodes a new lower bound for the dimension of a subfield subcode is given this bound improves the well known lower bound of p delsarte 1975 and coincides in many cases with the true dimension of the code alternant codes and geometric goppa codes are discussed as special cases

correspondence between the xxz model in roots of unity and the one dimensional quantum ising chain with different boundary conditions we consider the integrable xxz model with special open boundary conditions that renders its hamiltonian su 2 q symmetric and the one dimensional quantum ising model with four different boundary conditions we show that for each boundary condition the ising quantum chain is given exactly by the minimal model of integrable lattice theory lm 3 4 this theory is obtained as the result of the quantum group reduction of the xxz model at anisotropy q q 1 2 2 1 2 2 with a number of sites that depends on the type of imposed boundary condition

conformal anomaly and critical exponents of the spin 1 takhtajan babujian model the authors consider the critical behaviour of the spin 1 hamiltonian of the takhtajan babujian model the bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically the conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system the results strongly support the conjecture that the wess zumino witten non linear sigma model with topological charge k 2 is the underlying field theory for this statistical mechanics model

hybrid spline difference method for the burgers equation abstract this study developed a high accuracy hybrid spline difference method and deduced a difference equation that is very similar to finite difference method from the concept of spline difference as validated by nonlinear burgers equation the concept of difference made the computational process as simple as the finite difference method and easy to be implemented the free parameters 1 12 and 1 6 were combined in the concept of spline hybrid in order to increase the accuracy of the first and second derivatives of space from o h 2 of finite difference method to the o h 4 the accuracy was improved and the numerical oscillation with the increase in parameter r e was improved greatly

asymptotically fast group operations on jacobians of general curves abramovich d 1996 int math res notices p1005 aho a v 1975 design anal computer becker t 1993 graduate texts math v141 brawley j 2004 density primitixe el burgisserr p 1997 fundamentals pricnip v315 cantor dg 1987 math comput v48 p95 doi 10 2307 2007876 chow wl 1954 am j math v76 p453 doi 10 2307 2372585 coppersmith d 1990 j symb comput v9 p251 doi 10 1016 s0747 7171 08 80013 2 decker wolfram 1999 algorithmic algebra p187 eberly w 2000 j symb comput v29 p441 doi 10 1006 jsco 1999 0308 greg w 2002 adv math v172 p169 griffiths p 1994 principles algebraic hartshorne robin 1977 algebraic geometry hess f 1999 thesis technische u hess f 2002 j symb comput v33 p425 doi 10 1006 jsco 2001 0513 huang md 1994 j symb comput v18 p519 doi 10 1006 jsco 1994 1063 kemper g 2002 j symb comput v34 p229 doi 10 1006 jsco 2002 0560 kemper g 2004 math comput v73 p245 khurimakdisi k 2004 asymptotically fast lazarsfeld r 1989 sampling vector bund p500 pari group bord pari gp stein w modular forms databa volcheck e 1994 lect notes computer v877 p221

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

use residual correction method to calculate the upper and lower solutions of initial value problem abstract this article attempts to establish solutions monotonic relation with residuals of initial value problem through the concept of maximum principle for differential equations then discretizes the equation by the simple spline approximation for initial value problem converts the once complex inequation constraint mathematical programming problem into a simple problem of equation iteration by applying the new residual correction method for initial value problem put forth by this article and obtains the upper and lower solutions of initial value problem results from numerical validation indicate this method is accurate simple and fast the approximate solutions obtained can correctly analyze error range and the new method put forth hereby helps increase the accuracy of mean approximate solutions

operator content of the xxz chain the finite size scaling spectra of the xxz heisenberg chain are presented for even and odd numbers of sites respectively the operator content is given for free as well as for toroidal boundary conditions

integrable impurities for an open fermion chain employing the graded versions of the yang baxter equation and the reflection equations we construct two kinds of integrable impurities for a small polaron model with general open boundary conditions a we shift the spectral parameter of the local lax operator at arbitrary sites in the bulk and b we embed the impurity fermion vertex at each boundary of the chain the hamiltonians with different types of impurity terms are given explicitly the bethe ansatz equations as well as the eigenvalues of the hamiltonians are constructed by means of the quantum inverse scattering method in addition we discuss the ground state properties in the thermodynamic limit

the operator content of the exactly integrable su n magnets the operator content of the exactly integrable models associated with the su n lie algebras with periodic boundaries are studied the authors results were obtained from a numerical and analytical analysis of the associated bethe ansatz equations the resulting spectra indicate that the ferromagnetic and antiferromagnetic models have different operator content for n 2 being realizations of distinct modular invariant solutions

finite size scaling for correlations of quantum spin chains at criticality we study the finite size scaling behavior of two point correlation functions of translationally invariant many body systems at criticality we propose an efficient method for calculating the two point correlation functions in the thermodynamic limit from numerical data of finite systems our method is most effective when applied to a two dimensional classical system which possesses a conformal invariance by using this method with numerical data obtained from exact diagonalizations and monte carlo simulations we study the spin spin correlations of the quantum spin 1 2 and 3 2 antifierromagnetic chains in particular the logarithmic corrections to power law decay of the correlation of the spin 1 2 isotropic heisenberg antiferromagnetic chain are studied thoroughly we clarify the cause of the discrepancy in previous calculations for the logarithmic corrections our result strongly supports the field theoretic prediction based on the mappings to the wess zumino witten nonlinear model or the sine gordon model we also treat logarithmic corrections and crossover phenomena in the spin spin correlation of the spin 3 2 isotropic heisenberg antiferromagnetic chain our results are consistent with the affleck haldane prediction that the correlation of the spin 3 2 chain exhibits a crossover to the same asymptotic behavior as in the spin 1 2 chain

linear algebra algorithms for divisors on an algebraic curve we use an embedding of the symmetric dth power of any algebraic curve c of genus g into a grassmannian space to give algorithms for working with divisors on c using only linear algebra in vector spaces of dimension o g and matrices of size o g2 o g when the base field k is finite or if c has a rational point over k these give algorithms for working on the jacobian of c that require o g4 field operations arising from the gaussian elimination our point of view is strongly geometric and our representation of points on the jacobian is fairly simple to deal with in particular none of our algorithms involves arithmetic with polynomials we note that our algorithms have the same asymptotic complexity for general curves as the more algebraic algorithms in florian hess 1999 ph d thesis which works with function fields as extensions of k x however for special classes of curves hess algorithms are asymptotically more efficient than ours generalizing other known efficient algorithms for special classes of curves such as hyperelliptic curves cantor 1987 superelliptic curves galbraith paulus and smart 2002 and cab curves harasawa and suzuki 2000 in all those cases one can attain a complexity of o g2

the minimum distance of codes in an array coming from telescopic semigroups the concept of an error correcting array gives a new bound on the minimum distance of linear codes and a decoding algorithm which decodes up to half this bound this gives a unified point of view which explains several improvements on the minimum distance of algebraic geometric codes moreover it is explained in terms of linear algebra and the theory of semigroups only

spectrum of a duality twisted ising quantum chain the ising quantum chain with a peculiar twisted boundary condition is considered this boundary condition first introduced in the framework of the spin 1 2 xxz heisenberg quantum chain is related to the duality transformation which becomes a symmetry of the model at the critical point thus at the critical point the ising quantum chain with the duality twisted boundary is translationally invariant as in the case of the usual periodic or antiperiodic boundary conditions the complete energy spectrum of the ising quantum chain is calculated analytically for finite systems and the conformal properties of the scaling limit are investigated this provides an explicit example of a conformal twisted boundary condition and a corresponding generalized twisted partition function

the modified xxz heisenberg chain conformal invariance and the surface exponents of c 1 systems the authors present the operator content of the xxz chain in the presence of external fields the finite size scaling spectra can be expressed in terms of irreps of shifted u 1 kac moody algebras the shift depending on the external fields using an explicit feigin fuchs construction 1982 they project out from these spectra the operator content of c 1 systems with free fixed and mixed boundary conditions they also show how this projection mechanism works for a finite number of sites

error analysis of approximate solutions of non linear burgers equation this paper deals with application of the maximum principle for differential equations to the finite difference method for determining upper and lower approximate solutions of the non linear burgers equation and their error range in term of mathematical architecture the paper is based on the maximum principle for parabolic differential equations to establish monotonic residual relations of the burgers equation and in terms of numerical method it applies the finite difference method to discretize the equation followed by use of the proposed residual correction method for obtaining its optimal solutions under constraint conditions for inequalities derived by using this approach the upper and lower transient approximate solutions are not just useful in analyzing the range of the maximum possible error between them and the analytic solutions correctly and the numerical validations also indicate good accuracy in mean values of the upper and lower approximate solutions

majority coset decoding a majority coset decoding mcd procedure that can be applied to an arbitrary geometric code is discussed in general the basic algorithm for decoding of algebraic geometric codes does not correct up to the designed minimum distance in mcd a reduction step is added to the basic algorithm in case the basic algorithm fails a majority scheme is used to obtain an additional syndrome for the error vector thus a strictly smaller cost containing the error vector is obtained in this way the basic algorithm is applied to a decreasing chain of cosets and after finitely many steps the coset will be small enough for successful application of the basic algorithm

two dimensional semi infinite multicritical ising models the order parameter correlation functions of the z2 invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi infinite plane constrained to fixed or free boundary conditions these yield the corresponding universal surface exponents which distinguish the behaviour between even and odd critical models we also make explicit the interplay between duality and boundary conditions

lattice derivation of modular invariant partition functions on the torus the author expresses the partition functions of the ade lattice models on the torus in terms of partition function of six vertex models and which can be computed in the continuum limit thus the author recovers the partition function of minimal models with c 1 and new ones with c 1

the spectra of quantum chains with free boundary conditions and virasoro algebras at the critical point the spectra of quantum chains with periodic and twisted boundary conditions are described by irreducible representations of two virasoro algebras with the same central charge the authors show that in the case of free boundary conditions the spectra can be understood in terms of irreducible representations of a single virasoro algebra for the ising and the three state potts models the corresponding irreducible representations are identified

the lowest excitations in the spin s xxx magnet and conformal invariance the bethe ansatz equations for the integrable spin s isotropic heisenberg antiferromagnet are solved numerically at a finite number of sites n the vacuum and the lowest singlet and triplet solutions are presented for s 1 2 2 up to sn 240 through extrapolation of the finite size data the central charge and anomalous dimensions of the scaling operators for the underlying conformal field theory are calculated and found to agree with the expected theoretical values the status of the bethe string hypothesis about the structure of the solutions is discussed based on the obtained computer data up to s 9 2

the spectra of q state vertex models and related antiferromagnetic quantum spin chains some exactly solvable q state vertex models are investigated the author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome bethe ansatz the results are applied to related quantum spin chains of which two families are su q and so q invariant respectively various quantities are calculated e g energy momentum excitations and the correlation length for q 3 the su q invariant chain is the pure biquadratic spin 1 hamiltonian which turns out to be non critical the ground state energy the gap and the correlation length are given

cyclic representations of the periodic temperley lieb algebra complex virasoro representations and stochastic processes an dimensional representation of the periodic temperley lieb algebra tll x is presented it is also a representation of the cyclic group zn we choose x 1 and define a hamiltonian as a sum of the generators of the algebra acting in this representation this hamiltonian gives the time evolution operator of a stochastic process in the finite size scaling limit the spectrum of the hamiltonian contains representations of the virasoro algebra with complex highest weights the n 3 case is discussed in detail we discuss briefly the consequences of the existence of complex virasoro representations for the physical properties of the systems

on the parameters of goppa codes a proof of v d goppa s 1983 lower bound to the dimension of subfield subcodes of his geometric codes is given a result on the minimum distance of these subfield subcodes is also given that generalizes the well known bound minimum distance of gamma l g or 2 deg g x 1 for classical goppa codes gamma l g over the field f sub 2 with a square free goppa polynomial g g x

conformal invariance and the xxz chain with arbitrary spin abstract the critical properties of the anistropic heisenberg chain or xxz model with arbitrary spins s are studied the eigenspectrum of these models for finite chain length is calculated by solving their associated bethe ansatz equations the operator content with an even and odd number of sites is obtained by exploring the consequences of conformal invariance the results indicate the existence of critical lines governed by conformal theories with central charge c 3s 1 s and c 1 with critical exponents varying continuously with the anisotropy like in the 8 vertex model

finite size corrections for ground states of the xxz heisenberg chain the method of de vega and woynarovitch 1985 is used to calculate finite size corrections to the ground state energy in different sectors for the xxz heisenberg chain finite size scaling amplitudes and correction to scaling exponents in the critical region are derived using conformal invariance a scaling dimension x pi gamma 2 pi is extracted corresponding to the electric field operator in the 8 vertex model this confirms a conjecture of baxter and kelland 1974 finite size scaling properties near the kosterlitz thouless critical point delta 1 are discussed

operator content of the three state potts quantum chain the authors compute the lowest excitations of the spectra of the three state potts quantum chain with periodic and twisted boundary conditions these spectra can be understood in terms of eighteen irreducible representations of the virasoro algebra with c 4 5

the spin 1 2xxz heisenberg chain the quantum algebra uq sl 2 and duality transformations for minimal models the finite size scaling spectra of the spin 1 2 xxz heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c 1 including the unitary and nonunitary minimal series taking into account the half integer angular momentum sectors which correspond to chains with an odd number of sites in many cases leads to new spinor operators appearing in the projected systems these new sectors in the xxz chain correspond to new types of frustration lines in the projected minimal models the corresponding new boundary conditions in the hamiltonian limit are investigated for the ising model and the 3 state potts model and are shown to be related to duality transformations which are an additional symmetry at their self dual critical point by different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite xxz chain the observed degeneracies in the energy and momentummore spectra are shown to be the consequence of intertwining relations involving u sub q sl 2 quantum algebra transformations 35 refs 3 tabs less

the spin s xxz quantum chain with general toroidal boundary conditions the authors derive the operator content of the spin s xxz quantum chain with generalised toroidal boundary conditions compatible with the u 1 symmetry of the model these results are derived by solving numerically the associated bethe ansatz equations for finite chains and exploring the consequences of the conformal invariance of the infinite system they also show that as in the spin 1 2 case the conformal anomaly and dimensions of general extended su 2 algebras can be obtained from these spin s chains by choosing properly the coupling constant and the boundary condition

some finite size amplitudes and critical exponents for potts and ashkin teller quantum chains analytic expressions are derived for the leading finite size corrections to a class of energy eigenvalues of the potts and ashkin teller quantum chains making use of their equivalences with a modified xxz heisenberg chain assuming conformal invariance exact results are thence obtained for some bulk scaling dimensions and surface exponents in these models

conformal invariance and correction to finite size scaling applications to the three state potts model corrections to finite size scaling are determined numerically for several levels of the three state potts quantum chain with various boundary conditions it is found that the leading correction term behaves like wo in the case of periodic and twisted boundary conditions the coefficients of the n o term are determined by the three point correlation functions of the conformal theory

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

fractional strings hypothesis and non simple laced integrable models the author discusses the ground state and some elementary excitations of the bp non simple laced integrable models the zeros of the associated bethe ansatz equations are characterized by a special distribution in the complex plane which is different from the usual string hypothesis the introduction of this new solution makes it possible to calculate exactly various properties in the thermodynamic limit the finite size corrections to the eigenspectrum strongly suggest that the bp wess zumino witten novikov models are the underlying conformal field theory for these non simple laced models

excited states in the twisted xxz spin chain we compute the finite size spectrum for the spin chain with twisted boundary conditions for anisotropy in the regime and arbitrary twist the string hypothesis is employed for treating complex excitations the bethe ansatz equtions are solved within a coupled nonlinear integral equation approach with one equation for each type of string the root of unity quantum group invariant periodic chain reduces to the chain with a set of twist boundary conditions an integer multiple of for this model the restricted hilbert space corresponds to a unitary conformal field theory and we recover all primary states in the kac table in terms of states with specific twist and strings

critical behaviour of mixed heisenberg chains the critical behaviour of anisotropic heisenberg models with two kinds of antiferromagnetically exchange coupled centres are studied numerically by using finite size calculations and conformal invariance these models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism most of our results are centred in the mixed heisenberg chain where we have at even odd sites a spin su 2 operator interacting with a xxz like interaction anisotropy our results indicate universal properties for all these chains the whole phase where the models change from ferromagnetic to ferrimagnetic behaviour is critical along this phase the critical fluctuations are ruled by a c 1 conformal field theory of gaussian type the conformal dimensions and critical exponents along this phase are calculated by studying these models with several boundary conditions

polynomial time attack on wild mceliece over quadratic extensions we present a polynomial time structural attack against the mceliece system based on wild goppa codes defined over a quadratic finite field extension we show that such codes can be efficiently distinguished from random codes the attack uses this property to compute a filtration that is to say a family of nested subcodes which will reveal their secret algebraic description

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

centre of quantum group in roots of unity and the restriction of integrable models we show the connection between the extended centre of the quantum group in roots of unity and the restriction of the xxz model we also give explicit expressions for operators that respect the restriction and act on the state space of the restricted models the formulae for these operators are verified by explicit calculation for third degree roots they are conjectured to hold in the general case

decoding algebraic geometric codes up to the designed minimum distance a simple decoding procedure for algebraic geometric codes c sub omega d g is presented this decoding procedure is a generalization of peterson s decoding procedure for the bch codes it can be used to correct any d 1 2 or fewer errors with complexity o n sup 3 where d is the designed minimum distance of the algebraic geometric code and n is the codelength

a numerical solution of the burgers equation using cubic b splines in the present paper numerical solutions of the one dimensional burgers equation are obtained by a method based on collocation of cubic b splines over finite elements the accuracy of the proposed method is demonstrated by three test problems the numerical results are found in good agreement with exact solutions time space integration of the burgers equation yields a system of difference equation which is shown to be unconditionally stable

conformal invariance and critical exponents of the takhtajan babujian models the authors are concerned with the critical properties of antiferromagnetic takhtajan babujian models with spin s 1 3 2 and 2 the leading eigenenergies of this hamiltonian in a finite chain are calculated by investigating numerically and analytically the bethe ansatz equations for the finite system the critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite hamiltonian the appearance of logarithmic corrections produces poor estimates however a combination of analytical and numerical methods produces very good estimates their results strongly support the conjecture that the wess zumino witten novikov non linear sigma models with topological charge k 2s are the underlying field theories for these spin s statistical mechanics models

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

finite size corrections for spin s heisenberg chains and conformal properties the author compares recent results on finite size corrections for the isotropic xxx heisenberg chain and its integrable generalisations with former numerical and analytic calculations for the ground state and its lowest excitations leading and non leading terms are considered the analysis confirms the predictions of conformal invariance and sheds some new light on the fine structure of finite size corrections

convergence of finite size scaling renormalisation techniques abstract the rate of convergence of the transfer matrix finite size scaling or phenomenological renormalisation method is studied it is shown both heuristically and numerically that the convergence of estimates for exponents etc is governed asymptotically by the leading irrelevant variable scaling exponent the more rapid apparent convergence rates observed in many practical calculations for two dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms

relations between the coulomb gas picture and conformal invariance of two dimensional critical models partition functions of critical 2d models on a torus can be derived from their microscopic formulation and their free field representation in the continuum limit this is worked out explicitly for theo n andq state potts model forn orq integer we recover results obtained from conformal invariance but our procedure also extends to nonintegral values in the latter case the expansion on characters of the virasoro algebra involves real coefficients of either sign the operator content of both models is discussed in detail

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified

cryptanalysis of mceliece cryptosystem based on algebraic geometry codes and their subcodes we give polynomial time attacks on the mceliece public key cryptosystem based either on algebraic geometry ag codes or on small co dimensional subcodes of ag codes these attacks consist in the blind reconstruction either of an error correcting pair ecp or an error correcting array eca from the single data of an arbitrary generator matrix of a code an ecp provides a decoding algorithm that corrects up to d 1 g 2 errors where d denotes the designed distance and g denotes the genus of the corresponding curve while with an eca the decoding algorithm corrects up to d 1 2 errors roughly speaking for a public code of length n over mathbb f q these attacks run in o n 4 log n operations in mathbb f q for the reconstruction of an ecp and o n 5 operations for the reconstruction of an eca a probabilistic shortcut allows to reduce the complexities respectively to o n 3 varepsilon log n and o n 4 varepsilon compared with the previous known attack due to faure and minder our attack is efficient on codes from curves of arbitrary genus furthermore we investigate how far these methods apply to subcodes of ag codes