منابع مشابه
Shadow Bounds for Self-Dual Codes
Conway and Sloane have previously given an upper bound on the minimum distance of a singly-even self-dual binary code, using the concept of the shadow of a self-dual code. We improve their bound, finding that the minimum distance of a selfdual binary code of length n is at most 4bn=24c+4, except when nmod24 = 22 , when the bound is 4bn=24c + 6. We also show that a code of length a multiple of 2...
متن کاملThe Shadow Theory of Modular and Unimodular Lattices
and analogous bounds are established here for odd lattices satisfying certain technical conditions (which are trivial for N=1 and 2). For N>1 in (V), lattices meeting the new bound are constructed that are analogous to the ``shorter'' and ``odd'' Leech lattices. These include an odd associate of the 16-dimensional Barnes Wall lattice and shorter and odd associates of the Coxeter Todd lattice. A...
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Shadow Banking system, as an investment method, while being an integral part of the supervised banking system, is a rival for banks and governance institutions in financing and oversight. As a result, its development has created a situation for regulated institutions, which leads to concerns about the legal and regulatory responsibilities of the banking and financial system for investment not g...
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To an integral lattice L in the euclidean space (R, (, )), one associates the set of characteristic vectors v ∈ R with (v, x) ≡ (x, x) mod 2Z for all x ∈ L. They form a coset modulo 2L, where L = {v ∈ R | (v, x) ∈ Z ∀x ∈ L} is the dual lattice of L. Recall that L is called integral, if L ⊂ L and unimodular, if L = L. For a unimodular lattice, the square length of a characteristic vector is cong...
متن کاملShadow Mapping and Shadow Volumes: Recent Developments in Real-Time Shadow Rendering
In recent years , both Williams’ original Z-buffer shadow mapping algorithm [Williams 1978] and Crow’s shadow volumes [Crow 1977] have seen many variations, additions and enhancements, greatly increasing the visual quality and efficiency of renderings using these techniques. Additionally, the fast evolution of commodity graphics hardware allows for a nearly complete mapping of these algorithms ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00368-4