openness of versality via coherent functors we give a proof of openness of versality using coherent functors as an application we streamline artin s criterion for algebraicity of a stack we also introduce multi step obstruction theories employing them to produce obstruction theories for the stack of coherent sheaves the quot functor and spaces of maps in the presence of non atness

linear authentication codes bounds and constructions in this paper we consider a new class of unconditionally secure authentication codes called linear authentication codes or linear a codes we show that a linear a code can be characterized by a family of subspaces of a vector space over a finite field we then derive an upper bound on the size of the source space when other parameters of the system that is the sizes of the key space and the authenticator space and the deception probability are fixed we give constructions that are asymptotically close to the bound and show applications of these codes in constructing distributed authentication systems

minimal linear codes from characteristic functions minimal linear codes have interesting applications in secret sharing schemes and secure two party computation this paper uses characteristic functions of some subsets of mathbb f q to construct minimal linear codes by properties of characteristic functions we can obtain more minimal binary linear codes from known minimal binary linear codes which generalizes results of ding et al ieee trans inf theory vol 64 no 10 pp 6536 6545 2018 by characteristic functions corresponding to some subspaces of mathbb f q we obtain many minimal linear codes which generalizes results of ieee trans inf theory vol 64 no 10 pp 6536 6545 2018 and ieee trans inf theory vol 65 no 11 pp 7067 7078 2019 finally we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes

the period index problem for fields of transcendence degree 2 using geometric methods we prove the standard period index conjecture for the brauer group of a field of transcendence degree 2 over fp

the weight distribution of a class of linear codes from perfect nonlinear functions in this correspondence the weight distribution of a class of linear codes based on perfect nonlinear functions also called planar functions is determined the class of linear codes under study are either optimal or among the best codes known and have nice applications in cryptography

new constructions of subspace codes using subsets of mrd codes in several blocks a basic problem for the constant dimension subspace coding is to determine the maximal possible size mathrm a q n d k of a set of k dimensional subspaces in mathrm f q n such that the subspace distance satisfies d u v 2k 2 dim u cap v geq d for any two different subspaces u and v in this set we present two new constructions of constant dimension subspace codes using subsets of maximum rank distance mrd codes in several blocks this method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting mrd codes in these two constructions subsets of mrd codes with bounded ranks play an essential role the delsarte theorem about the rank distribution of mrd codes is an important ingredient to count codewords in our constructed constant dimension subspace codes we give many new lower bounds for mathrm a q n d k more than 110 new constant dimension subspace codes better than previously best known codes are constructed

almost perfect nonlinear power functions on gf 2 n the niho case almost perfect nonlinear apn mappings are of interest for applications in cryptography we prove for odd n and the exponent d 22r 2r 1 where 4r 1 0modn that the power functions xd on gf 2n is apn the given proof is based on a new class of permutation polynomials which might be of independent interest our result supports a conjecture of niho stating that the power function xd is even maximally nonlinear or in other terms that the crosscorrelation function between a binary maximum length linear shift register sequences of degree n and a decimation of that sequence by d takes on precisely the three values 1 1 2 n 1 2

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

cohomology and base change for algebraic stacks we prove that cohomology and base change holds for algebraic stacks generalizing work of brochard in the tame case we also show that hom spaces on algebraic stacks are represented by abelian cones generalizing results of grothendieck brochard olsson lieblich and roth starr to accomplish all of this we prove that a wide class of relative ext functors in algebraic geometry are coherent in the sense of m auslander

new families of almost perfect nonlinear power mappings a power mapping f x x sup d over gf p sup n is said to be differentially k uniform if k is the maximum number of solutions x spl isin gf p sup n of f x a f x b where a b spl isin gf p sup n and a spl ne 0 a 2 uniform mapping is called almost perfect nonlinear apn we construct several new infinite families of nonbinary apn power mappings

on proper coverings of artin stacks abstract we prove that every separated artin stack of finite type over a noetherian base scheme admits a proper covering by a quasi projective scheme an application of this result is a version of the grothendieck existence theorem for artin stacks

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

cartesian authentication codes from functions with optimal nonlinearity in this paper we present several classes of authentication codes using functions with perfect nonlinearity and optimum nonlinearity some of the authentication codes are optimal on the other hand these authentication codes are easy to implement due to their simple algebraic structures

multireceiver authentication code4 models bounds constructions and extensions multireceiver authentication codes allow one sender to construct an authenticated message for a group of receivers such that each receiver can verify authenticity of the received message in this paper we give a formal definition of multireceiver authentication codes derive information theoretic and combinatorial lower bounds on their performance and give new efficient and flexible constructions for such codes finally we extend the basic model to the case that multiple messages are sent and the case that the sender can be any member of the group

the hilbert stack let x s be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers we prove that there is an algebraic s stack the hilbert stack parameterizing proper a

stable points on algebraic stacks abstract this paper is largely concerned with constructing coarse moduli spaces for artin stacks the main purpose of this paper is to introduce the notion of stability on an arbitrary artin stack and construct a coarse moduli space for the open substack of stable points also we present an application to coherent cohomology of artin stacks

a generic construction of cartesian authentication codes in this paper a coding theory construction of cartesian authentication codes is presented the construction is a generalization of some known constructions within the framework of this generic construction several classes of authentication codes using certain classes of error correcting codes are described the authentication codes presented in this paper are better than known ones with comparable parameters it is demonstrated that the construction is related to certain combinatorial designs such as difference matrices and generalized hadamard matrices

low nonconvexity rank bilinear matrix inequalities algorithms and applications in robust controller and structure designs a branch and bound bb algorithm for solving a general class of bilinear matrix inequality bmi problems is proposed first linear matrix inequality lmi constraints are incorporated into bmi constraints in a special way to take advantage of useful information on nonconvex terms then the nonconvexity of the bmi is centralized in coupling constraints so that when the latter are omitted we get a relaxed lmi problem for computing lower bounds as in our previous developments the branching is performed in a reduced dimensional space of complicating variables this makes the approach practical even with a large dimension of overall variables applications of the algorithm to several test problems of robust control are discussed

on the cardinality of systematic authentication codes via error correcting codes in both open and private communication the participants face potential threats from a malicious enemy who has access to the communication channel and can insert messages impersonation attack or alter already transmitted messages substitution attack authentication codes a codes have been developed to provide protection against these threats in this paper we introduce a new distance called the authentication distance a distance and show that an a code can be described as a code for the a distance the a distance is directly related to the probability p sub s of success in a substitution attack we show how to transform an error correcting code into an a code and vice versa we further use these transformations to provide both upper and lower bounds on the size of the information to be authenticated and study their asymptotic behavior as examples of obtained results we prove that the cardinality of the source state space grows exponentially with the number of keys provided p sub s p sub i we generalize the square root bound given by gilbert macwilliams and sloane in 1979 and we provide very efficient constructions using concatenated reed solomon codes

almost perfect nonlinear power functions on gf 2 sup n the welch case we summarize the state of the classification of almost perfect nonlinear apn power functions x sup d on gf 2 sup n and contribute two new cases to prove these cases we derive new permutation polynomials the first case supports a well known conjecture of welch stating that for odd n 2m 1 the power function x sup 2m 3 is even maximally nonlinear or in other terms that the crosscorrelation function between a binary maximum length linear shift register sequence of degree n and a decimation of that sequence by 2 sup m 3 takes on precisely the three values 1 1 spl plusmn 2 sup m 1

optimal ferrers diagram rank metric codes optimal rank metric codes in ferrers diagrams are considered such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space first we consider rank metric anticodes and prove a code anticode bound for ferrers diagram rank metric codes the size of optimal linear anticodes is given four techniques and constructions of ferrers diagram rank metric codes are presented each providing optimal codes for different diagrams and parameters for which no optimal solution was known before the first construction uses maximum distance separable codes on the diagonals of the matrices the second one takes a subcode of a maximum rank distance code and the last two combine codes in small diagrams to a code in a larger diagram the constructions are analyzed and compared and unsolved diagrams are identified

monoidal infinity category of complexes from tannakian viewpoint in this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infty categories of quasi coherent complexes it can be viewed as a derived analogue of tannaka duality as a consequence we deduce that an algebraic stack satisfying a certain condition can be recovered from the symmetric monoidal stable infty category of quasi coherent complexes with tensor operation

coding for errors and erasures in random network coding the problem of error control in random linear network coding is considered a ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic motivated by the property that linear network coding is vector space preserving information transmission is modeled as the injection into the network of a basis for a vector space v and the collection by the receiver of a basis for a vector space u a metric on the projective geometry associated with the packet space is introduced and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space v capu is sufficiently large if the dimension of each codeword is restricted to a fixed integer the code forms a subset of a finite field grassmannian or equivalently a subset of the vertices of the corresponding grassmann graph sphere packing and sphere covering bounds as well as a generalization of the singleton bound are provided for such codes finally a reed solomon like code construction related to gabidulin s construction of maximum rank distance codes is described and a sudan style ldquolist 1rdquo minimum distance decoding algorithm is provided

noetherian approximation of algebraic spaces and stacks we show that every scheme resp algebraic space resp algebraic stack that is quasi compact with quasi finite diagonal can be approximated by a noetherian scheme resp algebraic space resp stack more generally we show that any stack which is etale locally a global quotient stack can be approximated examples of applications are generalizations of chevalley s serre s and zariski s theorems and chow s lemma to the non noetherian setting we also show that every quasi compact algebraic stack with quasi finite diagonal has a finite generically flat cover by a scheme

localized error correction in projective space in this paper we extend the localized error correction code introduced by l a bassalygo and coworkers from hamming space to projective space for constant dimensional localized error correction codes in projective space we have a lower bound and an upper bound of the capacity which are asymptotically tight when z x n z 2 where x z and n are dimensions of codewords error configurations and the ground space respectively we determine the capacity of nonconstant dimensional localized error correction codes when z n 3

p adic l functions and the coniveau filtration on chow groups we give evidence for the refined version of the bloch beilinson conjecture involving coniveau filtrations by studying several infinite families of cm motives indexed by the integers r 1 that are irreducible of hodge type 2r 1 0 0 2r 1 and whose l functions vanish at the center in each case we construct a corresponding algebraic cycle that is homologically trivial but nontrivial in the top graded piece for the coniveau filtration consequently we obtain new explicit examples of cycles that are nontorsion in the griffiths group the proof of the main result relies crucially on p adic hodge theoretic methods and in particular on the relation between images of homologically trivial cycles under the p adic abel jacobi map and the values of p adic l functions

robust output feedback controller design via local bmi optimization the problem of designing a globally optimal full order output feedback controller for polytopic uncertain systems is known to be a non convex np hard optimization problem that can be represented as a bilinear matrix inequality optimization problem for most design objectives in this paper a new approach is proposed to the design of locally optimal controllers it is iterative by nature and starting from any initial feasible controller it performs local optimization over a suitably defined non convex function at each iteration the approach features the properties of computational efficiency guaranteed convergence to a local optimum and applicability to a very wide range of problems furthermore a fast but conservative lmi based procedure for computing an initially feasible controller is also presented the complete approach is demonstrated on a model of one joint of a real life space robotic manipulator

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

on the relationships between perfect nonlinear functions and universal hash families in this paper the relationships between perfect nonlinear in brief pn functions and optimal universal hash families are discussed we point out the equivalence of constructions between them i e from pn functions one can obtain optimal universal hash families and vice versa as an application of our construction a message authentication code is proposed which provides better resistance to substitution attack than a known construction given by carlet et al in 2006 more generally the connections between functions with given differential uniformity and some universal hash families are studied

a rank metric approach to error control in random network coding the problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of rotter and kschischang a large class of constant dimension subspace codes is investigated it is shown that codes in this class can be easily constructed from rank metric codes while preserving their distance properties moreover it is shown that minimum distance decoding of such subspace codes can be reformulated as a generalized decoding problem for rank metric codes where partial information about the error is available this partial information may be in the form of erasures knowledge of an error location but not its value and deviations knowledge of an error value but not its location taking erasures and deviations into account when they occur strictly increases the error correction capability of a code if mu erasures and delta deviations occur then errors of rank t can always be corrected provided that 2t les d 1 mu delta where d is the minimum rank distance of the code for gabidulin codes an important family of maximum rank distance codes an efficient decoding algorithm is proposed that can properly exploit erasures and deviations in a network coding application where n packets of length m over f q are transmitted the complexity of the decoding algorithm is given by o dm operations in an extension field f qn

functorial reconstruction theorems for stacks abstract we study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes this is possible surprisingly often we show that many of the standard examples of moduli stacks are determined by their functors our methods seem to exhibit new anabelian style phenomena in the form of structures in the category of schemes that encode automorphism data in groupoids

an iterative approach to the optimal co design of linear control systems abstractthis paper investigates the optimal co design of both physical plants and control policies for a class of continuous time linear control systems the optimal co design of a specific linear control system is commonly formulated as a nonlinear non convex optimisation problem nnop and solved by using iterative techniques where the plant parameters and the control policy are updated iteratively and alternately this paper proposes a novel iterative approach to solve the nnop where the plant parameters are updated by solving a standard semi definite programming problem with non convexity no longer involved the proposed system design is generally less conservative in terms of the system performance compared to the conventional system equivalence based design albeit the range of applicability is slightly reduced a practical optimisation algorithm is proposed to compute a sub optimal solution ensuring the system stability and the convergence of the algorithm is established the effectiveness of

a luna etale slice theorem for algebraic stacks we prove that every algebraic stack locally of nite type over an algebraically closed eld with ane stabilizers isetale locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group the proof uses an equivariant version of artin s algebraization theorem proved in the appendix we provide numerous applications of the main theorems

optimal codesign of nonlinear control systems based on a modified policy iteration method this brief studies the optimal codesign of nonlinear control systems simultaneous design of physical plants and related optimal control policies nonlinearity of the optimal codesign problem could come from either a nonquadratic cost function or the plant after formulating the optimal codesign into a nonconvex optimization problem an iterative scheme is proposed in this brief by adding an additional step of system equivalence based policy improvement to the conventional policy iteration we have proved rigorously that the closed loop system performance can be improved after each step of the proposed policy iteration scheme and the convergence to a suboptimal solution is guaranteed it is also shown that under certain conditions this additional policy improvement step can be conducted by solving a quadratic programming problem the linear version of the proposed methodology is addressed in the context of linear quadratic regulator finally the effectiveness of the proposed methodology is illustrated through the optimal codesign of a load positioning system

logarithm cartesian authentication codes chanson ding and salomaa have recently constructed several classes of authentication codes using certain classes of functions in this paper we further extend that work by constructing two classes of cartesian authentication codes using the logarithm functions the codes constructed here involve the theory of cyclotomy and are better than a subclass of helleseth johansson s codes and bierbrauer s codes in terms of the maximum success probability with respect to the substitution attack

systematic authentication codes from highly nonlinear functions recently highly nonlinear functions have been successfully employed to construct authentication codes with and without secrecy in this paper we construct four classes of systematic authentication codes from perfect nonlinear functions and almost perfect nonlinear functions the systematic authentication codes presented in this paper are either better than existing codes or as good as the best codes known

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal

foncteur de picard d un champ algebrique resume in this article we study the picard functor and the picard stack of an algebraic stack we give a new and direct proof of the representability of the picard stack we prove that it is quasi separated and that the connected component of the identity is proper when the fibers of x are geometrically normal we study some examples of picard functors of classical stacks in an appendix we review the lisse etale cohomology of abelian sheaves on an algebraic stack

the linear programming approach to approximate dynamic programming the curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large scale stochastic control problems we study an efficient method based on linear programming for approximating solutions to such problems the approach fits a linear combination of pre selected basis functions to the dynamic programming cost to go function we develop error bounds that offer performance guarantees and also guide the selection of both basis functions and state relevance weights that influence quality of the approximation experimental results in the domain of queueing network control provide empirical support for the methodology

finiteness theorems for the picard objects of an algebraic stack abstract we prove some finiteness theorems for the picard functor of an algebraic stack in the spirit of sga 6 exp xii and xiii in particular we give a stacky version of raynaud s relative representability theorem we give sufficient conditions for the existence of the torsion component of the picard functor and for the finite generation of the neron severi groups or of the picard group itself we give some examples and applications in appendix a we prove the semicontinuity theorem for a non necessarily tame algebraic stack

constructions of authentication codes from algebraic curves over finite fields we present a new application of algebraic curves over finite fields to the constructions of universal hash families and unconditionally secure codes we show that the constructions derived from the garcia stichtenoth curves yield new classes of authentication codes and universal hash families which are substantially better than those previously known