(v, k, λ) Configurations and self-dual codes

The incidence matrix of a (v, k, λ) configuration is used to construct a (2v, v) and a (2v + 2, v + 1) self-dual code. If the incidence matrix is a circulant, the codes obtained are quasi-cyclic and extended quasi-cyclic, respectively. The weight distributions of some codes of this type are obtained.

Some new Results for Additive Self-Dual Codes over GF(4)

* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.

New Binary Extremal Self-Dual Codes of Lengths 50 and 52

* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995.

On Extremal Binary Doubly-Even Self-Dual Codes of Length 88*

In this paper we present 35 new extremal binary self-dual doubly-even codes of length 88. Their inequivalence is established by invariants. Moreover, a construction of a binary self-dual [88, 44, 16] code, having an automorphism of order 21, is given.

On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7

Николай Янков - Класифицирани са с точност до еквивалетност всички оптимални двоични самодуални [62, 31, 12] кодове, които притежават автоморфизъм от ред 7 с 8 независими цикъла при разлагане на независими цикли. Използвайки метода за конструиране на самодуални кодове, притежаващи автоморфизъм от нечетен прост ред е доказано, че съществуват точно 8 нееквивалентни такива кода. Три от получените кодове имат тегловна функция, каквато досега не бе известно да съществува.

New Binary $[70,35,12]$ Self-Dual and Binary $[72,36,12]$ Self-Dual Doubly-Even Codes

∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

The reverse self-dual serial cost-sharing rule

In this study we define a cost sharing rule for cost sharing problems. This rule is related to the serial cost-sharing rule defined by Moulin and Shenker (1992). We give some formulas and axiomatic characterizations for the new rule. The axiomatic characterizations are related to some previous ones provided by Moulin and Shenker (1994) and Albizuri (2010).

On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice

Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss. (C) 2009 Elsevier B.V. All rights reserved.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

A new spin-2 self-dual model in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Duality between non-commutative Yang-Mills-Chem-Simons and non-Abelian self-dual models

By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the non-commutative Yang-Mills-ChernSimons theory and the non-commutative, non-Abelian self-dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Manifestly covariant actions for D=4 self-dual Yang-Mills and D=10 super-Yang-Mills

Using an infinite number of fields, we construct actions for D = 4 self-dual Yang-Mills with manifest Lorentz invariance and for D = 10 super-Yang-Mills with manifest super-Poincare invariance. These actions are generalizations of the covariant action for the D = 2 chiral boson which was first studied by McClain, Wu, Yu and Wotzasek.

Self-dual super-Yang-Mills as a string theory in (x, 0) space

Different string theories in twistor space have recently been proposed for describing N = 4 super-Yang-Mills. In this paper, a string theory in (x, theta) space is constructed for self-dual N = 4 super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the d = 10 superstring.