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» Constructing Small-Bias Sets from Algebraic-Geometric Codes
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FOCS
2009
IEEE
13 years 11 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»
13 years 11 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 4 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»
13 years 11 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»
12 years 11 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