We study the conditions for the fivebrane worldvolume theory in D=11 to admit supersymmetric solitons with non-vanishing self-dual three-form. We construct some new soliton solutions consisting of “superpositions” of calibrated surfaces, self-dual strings and instantons.

We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.

Linear complementary dual codes (LCD) are linear codes satisfying C ∩C = {0}. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some asymptotic results are derived.

We construct new four-dimensional superstring vacua with extended superconformal symmetries. A non-trivial dilaton background implies the existence of Abelian killing symmetries. These are used to construct dual equivalent backgrounds in a way preserving the N = 2 superconformal invariance.

It is proved that for a system of spins σi = ±1 having an interaction energy − ∑ Kijσiσj with all theKij strictly positive, one can construct a dual formulation by associating a dual spin Sijk = ±1 to each triplet of distinct sites i, j and k. The dual interaction energy reads − ∑

We show that every uniformly asymptotically affine circle endomorphism has a uniformly asymptotically conformal (UAC) extension to the complex plane. Then we use the UAC extension to construct the dual dynamical system, the dual annulus, and the dual circle expanding map.

Starting from a generalization of a recent result on self-duality [15] we systematically analyze self-dual models. We find a criterion to judge whether a given model is self-dual or not. With this tool we construct some new self-dual pairs, focussing on examples with exceptional gauge groups. ∗Work supported by DFG

In [H. Taniguchi, On d-dimensional dual hyperovals in PG(2d,2), Innov. Incidence Geom., in press], we construct d-dimensional dual hyperovals in PG(2d,2) from quasifields of characteristic 2. In this note, we show that, if d-dimensional dual hyperovals in PG(2d,2) constructed from nearfields are isomorphic, then those nearfields are isomorphic. Some results on dual hyperovals constructed from q...

In this paper, we study self-dual codes over Z2× (Z2+uZ2), where u 2 = 0. Three types of self-dual codes are defined. For each type, the possible values α, β such that there exists a code C ⊆ Z2×(Z2+uZ2) β are established. We also present several approaches to construct self-dual codes over Z2 × (Z2 + uZ2). Moreover, the structure of two-weight self-dual codes is completely obtained for α · β 6...

In this correspondence, we study optimal self-dual codes and Type IV self-dual codes over the ring F2 + vF2 of order 4. We give improved upper bounds on minimum Hamming and Lee weights for such codes. Using the bounds, we determine the highest minimum Hamming and Lee weights for such codes of lengths up to 30. We also construct optimal self-dual codes and Type IV self-dual codes.