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COMBINATORICS
1998
60views more  COMBINATORICS 1998»
13 years 4 months ago
Finite Vector Spaces and Certain Lattices
The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF(q). When q is prime, we prove that Gn(q) is equal to...
Thomas W. Cusick
JCT
2010
85views more  JCT 2010»
12 years 12 months ago
Symmetric bilinear forms over finite fields of even characteristic
Let Sm be the set of symmetric bilinear forms on an m-dimensional vector space over GF(q), where q is a power of two. A subset Y of Sm is called an (m, d)-set if the difference of...
Kai-Uwe Schmidt
SODA
2012
ACM
217views Algorithms» more  SODA 2012»
11 years 7 months ago
Deterministic construction of an approximate M-ellipsoid and its applications to derandomizing lattice algorithms
We give a deterministic O(log n)n -time and space algorithm for the Shortest Vector Problem (SVP) of a lattice under any norm, improving on the previous best deterministic nO(n) -...
Daniel Dadush, Santosh Vempala
CVPR
2008
IEEE
14 years 7 months ago
Spectral methods for semi-supervised manifold learning
Given a finite number of data points sampled from a low-dimensional manifold embedded in a high dimensional space together with the parameter vectors for a subset of the data poin...
Zhenyue Zhang, Hongyuan Zha, Min Zhang