In this work, quadratic double and quadratic bordered double circulant constructions are applied to F4 + uF4 as well as F4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension theorems as well as the ring extension version are used to obtain 7 extremal self-dual binary codes of length 58, 24 extremal self-dual binary codes of length 66 and...

We prove uniqueness theorems for asymptotically flat, stationary, extremal, vacuum black hole solutions, in four and five dimensions with one and two commuting rotational Killing fields respectively. As in the non-extremal case, these problems may be cast as boundary value problems on the two dimensional orbit space. We show that the orbit space for solutions with one extremal horizon is homeom...

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges assoc...

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in Q( √ −3) are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3. In 1978 W. Feit [10] classified the unimodular hermitian lattices of dimensions up to 12 over the ring Z[ω] of Eisenstein integers, where ω is a primitive third root of unity. Th...

This paper presents explicit equations over Q for 32 extremal semistable elliptic K3 surfaces. They are realized as pull-back of non-semi-stable extremal rational elliptic surfaces via base change. Together with work of J. Top and N. Yui which exhibited the same procedure for the semi-stable extremal rational elliptic surfaces, this exhausts this approach to produce extremal semi-stable ellipti...

A classification of extremal double circulant self-dual codes of lengths up to 88 is known. We demonstrate that there is no extremal double circulant self-dual code of length 90. We give a classification of double circulant self-dual [90, 45, 14] codes. In addition, we demonstrate that every double circulant self-dual [90, 45, 14] code has no extremal selfdual neighbor of length 90. Finally, we...

The purpose of this paper is to analyse a class of quadratic extremal problems defined on various Hilbert spaces of analytic functions, thereby generalizing an extremal problem on the Dirichlet space which was solved by S.D. Fisher. Each extremal problem considered here is shown to be connected with a system of orthogonal polynomials. The orthogonal polynomials then determine properties of the ...

We consider a class of extremal and non-extremal four-dimensional black-hole solutions occuring in toroidally compactiied heterotic string theory, whose ten-dimensional interpretation involves a Kaluza-Klein monopole and a ve-brane. We show that these four-dimensional solutions can be connected to extremal and non-extremal two-dimensional heterotic black-hole solutions through a change in the a...