منابع مشابه
The Projective Geometry of the Gale Transform
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points fail to satisfy the minimal free resolution conjecture (see Eisenbud-Popescu [1996]). In this paper we reexamine the Gale transform in the light of modern a...
متن کاملSome recent results in finite geometry and coding theory arising from the Gale transform
The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, and so on. We give a brief survey—from a finite geometry point of view—on the algebraic and geometrical implications of the Gale transform with emphasis on its applications to coding theory, and describe some...
متن کامل. A G ] 2 3 Ju l 1 99 8 The Projective Geometry of the Gale Transform
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points fail to satisfy the minimal free resolution conjecture (see Eisenbud-Popescu [1996]). In this paper we reexamine the Gale transform in the light of modern a...
متن کاملLinear Difference Equations, Frieze Patterns and Combinatorial Gale Transform
We study the space of linear di↵erence equations with periodic coe cients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of combinatorial Gale transform which is a duality between periodic di↵erence equations of di↵erent orde...
متن کاملFinite Fourier Transform, Circulant Matrices, and the Fast Fourier Transform
Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.08.019