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» Constructing Small-Bias Sets from Algebraic-Geometric Codes
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FOCS
2009
IEEE
14 years 4 months ago
Constructing Small-Bias Sets from Algebraic-Geometric Codes
We give an explicit construction of an -biased set over k bits of size O k 2 log(1/ ) 5/4 . This improves upon previous explicit constructions when is roughly (ignoring logarith
Avraham Ben-Aroya, Amnon Ta-Shma
APPROX
2009
Springer
156views Algorithms» more  APPROX 2009»
14 years 4 months ago
Small-Bias Spaces for Group Products
Small-bias, or -biased, spaces have found many applications in complexity theory, coding theory, and derandomization. We generalize the notion of small-bias spaces to the setting ...
Raghu Meka, David Zuckerman
AAECC
2004
Springer
83views Algorithms» more  AAECC 2004»
13 years 9 months ago
Bounding the Trellis State Complexity of Algebraic Geometric Codes
Abstract. Let C be an algebraic geometric code of dimension k and length n constructed on a curve X over Fq. Let s(C) be the state complexity of C and set w(C) := min{k, n-k}, the ...
Carlos Munuera, Fernando Torres
ICC
2007
IEEE
127views Communications» more  ICC 2007»
14 years 4 months ago
Efficient Factorisation Algorithm for List Decoding Algebraic-Geometric and Reed-Solomon Codes
— The list decoding algorithm can outperform the conventional unique decoding algorithm by producing a list of candidate decoded messages. An efficient list decoding algorithm fo...
L. Chen, Rolando A. Carrasco, Martin Johnston, E. ...
JMLR
2010
119views more  JMLR 2010»
13 years 4 months ago
The Coding Divergence for Measuring the Complexity of Separating Two Sets
In this paper we integrate two essential processes, discretization of continuous data and learning of a model that explains them, towards fully computational machine learning from...
Mahito Sugiyama, Akihiro Yamamoto