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...

Our purpose is to find an upper bound for the length of s-extremal codes over F2 (resp. F4) when d ≡ 2 (mod 4) (resp. d odd). This question is left open in [6], [2]. More precisely, we show that there is no s-extremal binary code of length n ≥ 21d− 82 if d > 6 and d ≡ 2 (mod 4). Similarly we show that there is no s-extremal additive F4 code of length n ≥ 13d− 26 if d > 1 and d is odd. We also d...

We consider the thermodynamics of the near-extremal NS5-brane in type IIA string theory. The central tool we use is to map phases of six-dimensional Kaluza-Klein black holes to phases of near-extremal M5-branes with a transverse circle in eleven-dimensional supergravity. By S-duality these phases correspond to phases of the near-extremal type IIA NS5-brane. One of our main results is that in th...

Consider a compact Kähler manifold X with a simple normal crossing divisor D, and define Poincaré type metrics on X\D as Kähler metrics on X\D with cusp singularities along D. We prove that the existence of a constant scalar curvature (resp. an extremal) Poincaré type Kähler metric on X\D implies the existence of a constant scalar curvature (resp. an extremal) Kähler metric, possibly of Poincar...

A ternary permutation constraint satisfaction problem (CSP) is specified by a subset Π of the symmetric group S3. An instance of such a problem consists of a set of variables V and a set of constraints C, where each constraint is an ordered triple of distinct elements from V . The goal is to construct a linear order α on V such that, for each constraint (a, b, c) ∈ C, the ordering of a, b, c in...

We study stretched horizons of the type AdS2×S for certain spherically symmetric extremal small black holes in type IIA carrying only D0-brane charge making use of Sen’s entropy function formalism for higher derivative gravity. A scaling argument is given to show that the entropy of this class of black holes for large charge behaves as √ |q| where q is the electric charge. The leading order res...

We intend to give a classification of smooth nondegenerate projective varieties admitting extremal or next to extremal curvilinear secant subspaces. Gruson, Lazarsfeld and Peskine classified all projective integral curves with extremal secant lines. On the other hand, if a locally Cohen-Macaulay variety Xn ⊂ Pn+e of degree d meets with a linear subspace L of dimension β at finite points, then l...

The study of extremal Kähler metric is initiated by the seminal works of Calabi [4], [5]. Let (M, [ω]) be a compact Kähler manifold with fixed Kähler class [ω]. For any Kähler metrics g in the fixed Kähler class [ω], the Calabi energy C(g) is defined as C(g) = M s 2 dµ, where s is the scalar curvature of g. The extremal Kähler metric is the critical point of the Calabi energy. The Euler-Lagrang...