self dual codes with an automorphism of order 11 using a method for constructing self dual codes having an automorphism of odd prime order we classify up to equivalence all binary self dual codes with an automorphism of order 11 with 6 cycles and minimum distance 12 this classification gives new 72 36 12 codes with weight enumerator that was previously not obtained as well as many 66 33 12 68 34 12 and 70 35 12 codes with new values of the parameters in their respective weight enumerators

doubly even self dual code of length 96 we prove that 23 11 and 7 do not divide the order of the automorphism group of a binary 96 48 20 doubly even self dual code we construct 25 new inequivalent binary 96 48 16 doubly even self dual codes via an automorphism of order 23

the automorphism group of a self dual 72 36 16 code does not contain z_ 4 it has been proven in a series of works that the order of the automorphism group of a self dual binary 72 36 16 code does not exceed five up to equivalence we obtain a parametrization of all self dual binary codes of length 72 with automorphism of order four which can be extremal we use extensive computations in magma and on a supercomputer to show that the automorphism group of an extremal self dual binary code of length 72 does not have an element of order four

on the 24 12 10 quaternary code and binary codes with an automorphism having two cycles a general decomposition theorem is given for codes over finite fields which have an automorphism of a given type such codes can be decomposed as direct sums of subcodes which may be viewed as shorter length codes over extension fields if such a code is self dual sometimes the subcodes are also this decomposition is applied to prove that the self dual 24 12 10 quaternary code has no automorphism of order 3 this decomposition is also applied to count the number of equivalent 2r r and 2r 2r 1 self dual binary codes with an automorphism of prime order r

on covering radii and coset weight distributions of extremal binary self dual codes of length 56 we present a method to determine the complete coset weight distributions of doubly even binary self dual extremal 56 28 12 codes the most important steps are 1 to describe the shape of the basis for the linear space of rigid jacobi polynomials associated with such codes in each index i 2 to describe the basis polynomials for the coset weight enumerators of the assigned coset weight i by means of rigid jacobi polynomials of index i the multiplicity of the cosets of weight i have a connection with the frequency of the rigid reference binary vectors v of weight i for the jacobi polynomials this information is sufficient to determine the complete coset weight distributions determination of the covering radius of the codes is an immediate consequence of this method one important practical advantage of this method is that it is enough to get information on 8190 codewords of weight 12 minimal weight words in each such code for computing every necessary information

locally optimum detection of signals in a generalized observation model the random signal case locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal dependent and multiplicative noise it is shown that the locally optimum random signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model examples of explicit results for the locally optimum detector test statistics are given for some typical cases both asymptotic and finite sample size performances of the locally optimum detectors are considered and compared with those of other standard detector structures

type ii codes over f sub 2 uf sub 2 the alphabet f sub 2 uf sub 2 is viewed here as a quotient of the gaussian integers by the ideal 2 self dual f sub 2 uf sub 2 codes with lee weights a multiple of 4 are called type ii they give even unimodular gaussian lattices by construction a while type i codes yield unimodular gaussian lattices construction b makes it possible to realize the leech lattice as a gaussian lattice there is a gray map which maps type ii codes into type ii binary codes with a fixed point free involution in their automorphism group combinatorial constructions use weighing matrices and strongly regular graphs gleason type theorems for the symmetrized weight enumerators of type ii codes are derived all self dual codes are classified for length up to 8 the shadow of the type i codes yields bounds on the highest minimum hamming and lee weights

automorphisms of order 2p in binary self dual extremal codes of length a multiple of 24 let c be a binary self dual code with an automorphism g of order 2p where p is an odd prime such that gp is a fixed point free involution if c is extremal of length a multiple of 24 all the involutions are fixed point free except the golay code and eventually putative codes of length 120 connecting module theoretical properties of a self dual code c with coding theoretical ones of the subcode c gp which consists of the set of fixed points of gp we prove that c is a projective f2 g module if and only if a natural projection of c gp is a self dual code we then discuss easy to handle criteria to decide if c is projective or not as an application we consider in the last part extremal self dual codes of length 120 proving that their automorphism group does not contain elements of order 38 and 58

the automorphism group of a binary self dual doubly even 72 36 16 code is solvable in this correspondence we prove that the automorphism group of a putative binary self dual doubly even 72 36 16 code is solvable moreover its order is 5 7 10 14 56 or a divisor of 72

on the automorphism group of a doubly even 72 36 16 code we prove that a putative doubly even 72 36 16 code has no automorphism of order 3 with fixed points moreover such a code has no automorphism of an odd order greater than 7 eventually we prove that 25 and 49 do not divide the order of its automorphism group

fourth power residue double circulant self dual codes quadratic residue codes are a well known class of codes in this paper we consider the constructions of self dual codes by higher power residues especially fourth power residues new infinite families of self dual codes over gf 2 gf 3 gf 4 gf 8 and gf 9 are introduced some of them have better minimum weight than previously known codes we also give general results related to the automorphism group of some of these codes

asymptotically optimum detection of a weak signal sequence with random time delays the problem of designing asymptotically optimum detectors for a weak signal sequence with random time delays in the presence of a white gaussian noise is considered the multidimensional probability distribution of the time delays is assumed to be known as a result of asymptotic analysis of the log likelihood ratio the asymptotically optimum linear or quadratic detectors and their probability distributions and efficiencies are found

automorphisms of extremal self dual codes let c be a binary extremal self dual code of length n 48 we prove that for each aut c of prime order p 5 the number of fixed points in the permutation action on the coordinate positions is bounded by the number of p cycles it turns out that large primes p i e n p small seem to occur in aut c very rarely examples are the extended quadratic residue codes we further prove that doubly even extended quadratic residue codes of length n p 1 are extremal only in the cases n 8 24 32 48 80 and 104

on the automorphism group of a binary self dual doubly even 72 36 16 code we prove that the automorphism group of a binary self dual doubly even 72 36 16 code has order 5 7 10 14 or d where d divides 18 or 24 or it is a4 c3

extremal binary self dual codes in this correspondence we investigate binary extremal self dual codes numerous extremal self dual codes and interesting self dual codes with minimum weight d 14 and 16 are constructed in particular the first extremal type i 86 43 16 code and new extremal self dual codes with weight enumerators which were not previously known to exist for lengths 40 50 52 and 54 are constructed we also determine the possible weight enumerators for extremal type i codes of lengths 66 100

on the structure of binary self dual codes having an automorphism of order a square of an odd prime we describe a method for constructing binary self dual codes having an automorphism of order p sup 2 for an odd prime p using this method we classify the optimal self dual codes of lengths 36 spl les n spl les 44 and n 54 having an automorphism of order 9 we obtain all self dual 56 28 12 58 29 10 and 60 30 12 codes having an automorphism of order 9 without cycles of length 3 some of the constructed codes of lengths 54 58 and 60 have weight enumerators for which the existence of codes was not known before

17 does not divide the order of the group of a 72 36 16 doubly even code corresp it is an interesting open question whether an extremal 72 36 16 doubly even code c exists in 3 the odd prime numbers which can divide the order of the group of c were determined the largest of these 23 was eliminated by finding weight 12 vectors in 384 codes 8 the next largest prime remaining is 17 it is shown that 17 is also not possible by reducing the problem to the consideration of 16 17 3 codes and then finding a weight 12 vector by computer in each of these codes

a simple slp algorithm for solving a class of nonlinear programs successive linear programming slp algorithms solve nonlinear optimization problems via a sequence of linear programs we present an approach for a special class of nonlinear programming problems which arise in multiperiod coal blending the class of nonlinear programming problems and the solution approach considered in this paper are quite different from previous work the algorithm is very simple easy to apply and can be applied to as large a problem as the linear programming code can handle the quality of solution produced by the proposed algorithm is discussed and the results of some test problems in the real world environment are provided

a method for constructing self dual codes with an automorphism of order 2 in this paper we investigate binary self dual codes with an automorphism of order 2 with c cycles and f fixed points a method for constructing such codes using self orthogonal codes of length c and self dual codes of length f is presented we apply this method to construct extremal self dual codes of lengths 40 42 44 52 54 and 58 some of them have weight enumerators for which self dual codes were previously not known to exist we prove that there do not exist self dual 50 25 10 and 96 48 20 codes with an automorphism of order 2 with f fixed points for f 0 in their automorphism groups

cubic self dual binary codes we study binary self dual codes with a fixed point free automorphism of order three all binary codes of that type can be obtained by a cubic construction that generalizes turyn s we regard such cubic codes of length 3 spl lscr as codes of length spl lscr over the ring f sub 2 spl times f sub 4 classical notions of type ii codes shadow codes and weight enumerators are adapted to that ring two infinite families of cubic codes are introduced new extremal binary codes in lengths spl les 66 are constructed by a randomized algorithm necessary conditions for the existence of a cubic 72 36 16 type ii code are derived

some new extremal codes of lengths 76 and 78 we find new extremal 76 38 14 and 78 39 14 binary self dual codes the code of length 76 is the first known self dual code with these parameters it is shadow extremal and the shortest known self dual code with minimal distance 14 it has an automorphism of order 19 without fixed coordinates the code of length 78 has a new weight enumerator and an automorphism of order 19 with two fixed coordinates

new binary singly even self dual codes in this paper we construct new binary singly even self dual codes with larger minimum weights than the previously known singly even self dual codes for several lengths several known construction methods are used to construct the new self dual codes

a method for constructing inequivalent self dual codes with applications to length 56 necessary and sufficient conditions are presented for two doubly even codes with an automorphism of odd prime order to be equivalent under certain assumptions for the codes as an application we obtain all extremal doubly even codes of length 56 with an automorphism of order 13 sixteen such codes are inequivalent

nonlinear optimization by successive linear programming successive linear programming slp which is also known as the method of approximation programming solves nonlinear optimization problems via a sequence of linear programs this paper reports on promising computational results with slp that contrast with the poor performance indicated by previously published comparative tests the paper provides a detailed description of an efficient reliable slp algorithm along with a convergence theorem for linearly constrained problems and extensive computational results it also discusses several alternative strategies for implementing slp the computational results show that slp compares favorably with the generalized reduced gradient code grg2 and with minos grg it appears that slp will be most successful when applied to large problems with low degrees of freedom

monomials of orders 7 and 11 cannot be in the group of a 24 12 10 self dual quaternary code corresp it is an interesting open question whether a self dual quaternary 24 12 10 code c exists it was shown by conway and pless that the only primes which can be orders of permutations in the group of c are 11 7 and 3 in this correspondence we eliminate 11 and 7 not only as permutations but also as orders of monomials in the group of c this is done by reducing the problems to the consideration of several codes and finding low weight vectors in these codes

on extremal self dual quaternary codes of lengths 18 to 28 ii a general decomposition theorem is given for self dual codes over finite fields that have a permutation automorphism of a given form such a code can be decomposed as a direct sum of subcodes that may be viewed as shorter length codes over extension fields where the dual of each direct summand is also a direct summand situations in which it is easy to distinguish such codes are also presented these results are used to enumerate some of the extremal quaternary self dual codes of lengths 18 20 22 26 and 28

on extremal self dual ternary codes of lengths 28 to 40 the extremal self dual ternary codes of lengths 28 32 and 36 with monomial automorphisms of prime order r or 5 and of length 40 with monomial automorphisms of prime order r 5 are enumerated for each length and prime considered all inequivalent extremal codes with an automorphism of that order are found

on the automorphism group of a putative code a long standing open question in coding theory is whether a binary self dual 72 36 16 code exists it was shown recently that the automorphism group order of such code is equal to 2imiddot3 jmiddot5middot7 2imiddot3jmiddot7 2imiddot3jmiddot5 or 2imiddot3 j for some nonnegative integers i and j we show that the group order is not a multiple of 35 and find that only 22 orders are possible

binary self dual codes with automorphisms of composite order in this paper we present some results concerning a decomposition of binary self dual codes having an automorphism of an order which is the product of two odd prime numbers these results are applied to construct self dual 72 36 12 codes with an automorphism of order 15 furthermore it is proved that the automorphism group of a putative binary extremal self dual 72 36 16 code contains at most 28 nontrivial types of automorphisms of odd order a complete list of these possible types of automorphisms is presented

new extremal self dual codes of lengths 42 and 44 all extremal binary self dual codes of lengths 42 and 44 which have an automorphism of order 5 with eight independent cycles are obtained up to equivalence there are 109 inequivalent 42 21 8 codes with such an automorphism all 44 22 8 codes that are obtained have 29 different weight enumerators

external theory for stochastic processes abstract the purpose of this paper is to provide an overview of the asymptotic distributional theory of extreme values for a wide class of dependent stochastic sequences and continuous parameter processes the theory contains the standard classical extreme value results for maxima and extreme order statistics as special cases but is richer on account of the diverse behavior possible under dependence in both discrete and continuous time contexts emphasis is placed on stationary cases but other important classes e g mark of sequences are included significant ideas and methods are described rather than details and in particular the nature and role of important underlying point processes such as exceedances and upcrossings are emphasized applications are given to particular classes of process e g normal moving average and connections with related theory such as convergence of sums are indicated

successive linear programming at exxon successive linear programming slp has been used extensively in the refining and petrochemical industries for over 20 years this paper concentrates on some recent work at exxon to unify the treatment of nonlinear terms in mostly linear models we first discuss the source of nonlinearities in refining and petrochemical problems and propose a multiplicative formulation for the linearized subproblems to be solved by slp we then describe a slp algorithm which is shown to be related to the concept of trust regions finally we present an example formulation and computational results for a series of large industrial applications

23 does not divide the order of the group of a 72 36 16 doubly even code corresp an interesting open question is whether a 72 36 16 doubly even code c exists in 3 the odd prime numbers which can divide the order of the group of c were determined and 23 is the largest of these twenty three is eliminated by reducing the problem to the consideration of 348 codes each of which is shown to have minimum weight 12 or less one of these codes denoted by c arises from the a x b x a b x construction where a and b are in one quadratic residue code and x is in the other the weight distribution of c is given

binary self dual codes of lengths 52 to 60 with an automorphism of order 7 or 13 all binary n n 2 optimal self dual codes for length 52 n 60 with an automorphism of order 7 or 13 are classified up to equivalence two of the constructed 54 27 10 codes have weight enumerators that were not previously known to exist there are also some 58 29 10 codes with new values of the parameters in their weight enumerator

a 72 36 16 doubly even code does not have an automorphism of order 11 corresp we prove that there does not exist a 72 36 16 doubly even code with an automorphism of order 11 if such a code exists it can be decomposed as a direct sum of two codes one can be viewed as a self dual 12 6 4 binary code and the other a self dual 6 3 4 code over f 1024 this is shown to be impossible

the existence of certain extremal 54 27 10 self dual codes some new extremal binary 54 27 10 self dual codes are constructed using automorphisms of order 7

the extended quadratic residue code is the only 48 24 12 self dual doubly even code an extremal self dual doubly even binary n k d code has a minimum weight d 4 spl lfloor n 24 spl rfloor 4 of such codes with length divisible by 24 the golay code is the only 24 12 8 code the extended quadratic residue code is the only known 48 24 12 code and there is no known 72 36 16 code one may partition the search for a 48 24 12 self dual doubly even code into three cases a previous search assuming one of the cases found only the extended quadratic residue code we examine the remaining two cases separate searches assuming each of the remaining cases found no codes and thus the extended quadratic residue code is the only doubly even self dual 48 24 12 code

automorphisms of codes with applications to extremal doubly even codes of length 48 general results on automorphisms of self dual binary codes are given these results are applied to the study of extremal self dual doubly even binary codes of length 48 the main theorem proved is that an extremal self dual doubly even code of length 48 with a nontrivial automorphism of odd order is equivalent to the extended quadratic residue code interesting constructions of the binary extended golay code as well as a conjecture about a possible connection between an extremal self dual doubly even code of length 72 and an extremal quaternary code of length 24 arc yielded by techniques used in the proof

a note on the solution of bilinear programming problems by reduction to concave minimization we present a new algorithm for solving the bilinear programming problem by reduction to concave minimization this algorithm is finite does not assume the boundedness of the constraint set and uses an efficient procedure for checking whether a concave function is bounded below on a given halfline some preliminary computational experience with a computer code for implementing the algorithm on a microcomputer is also reported

the automorphism group of a self dual 72 36 16 binary code does not contain elements of order 6 the existence of an extremal code of length 72 is a long standing open problem let c be a putative extremal code of length 72 and suppose that c has an automorphism g of order 6 we show that c as an bbf2 g module is the direct sum of two modules it is easy to determine one of them while the other one has a very restrictive structure we use this fact to do an exhaustive search and we do not find an extremal code this proves that the automorphism group of an extremal code of length 72 does not contain elements of order 6

on extremal self dual codes of length 96 let c be a binary extremal self dual code of length 96 we prove that an automorphism of c of order 3 has 6 or no fixed points and an automorphism of order 5 has 6 fixed points moreover if all automorphisms of order 3 are fixed point free then aut c is solvable and its order divides 253 or 255 or aut c is the alternating group a5 which is the only possible group of order 60 furthermore aut c 20 or 40 cannot occur

a putative doubly even 72 36 16 code does not have an automorphism of order 9 in this paper we prove that there does not exist a binary self dual doubly even code with an automorphism of order 9 to do so we apply a method for constructing binary self dual codes possessing an automorphism of order for an odd prime

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen