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AAECC
2002
Springer
132views Algorithms» more  AAECC 2002»
11 years 6 months ago
Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers
It is shown that a q-periodic sequence over the finite field Fq passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity...
Harald Niederreiter, Arne Winterhof
AAECC
2002
Springer
126views Algorithms» more  AAECC 2002»
11 years 6 months ago
Toric Varieties Hirzebruch Surfaces and Error-Correcting Codes
Abstract. For any integral convex polytope in R2 there is an explicit construction of an error-correcting code of length (q - 1)2 over the finite field Fq, obtained by evaluation o...
Johan P. Hansen
JOC
2006
103views more  JOC 2006»
11 years 6 months ago
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2
We present an algorithm to compute the zeta function of an arbitrary hyperelliptic curve over a finite field Fq of characteristic 2, thereby extending the algorithm of Kedlaya for ...
Jan Denef, Frederik Vercauteren
CORR
2010
Springer
99views Education» more  CORR 2010»
11 years 6 months ago
Security in Distributed Storage Systems by Communicating a Logarithmic Number of Bits
Abstract--We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that a...
Theodoros K. Dikaliotis, Alexandros G. Dimakis, Tr...
COCO
2008
Springer
100views Algorithms» more  COCO 2008»
11 years 8 months ago
Detecting Rational Points on Hypersurfaces over Finite Fields
We study the complexity of deciding whether a given homogeneous multivariate polynomial has a nontrivial root over a finite field. Given a homogeneous algebraic circuit C that com...
Swastik Kopparty, Sergey Yekhanin
DCC
2002
IEEE
12 years 6 months ago
Subcodes of the Projective Generalized Reed-Muller Codes Spanned by Minimum-Weight Vectors
We use methods of Mortimer [19] to examine the subcodes spanned by minimumweight vectors of the projective generalized Reed-Muller codes and their duals. These methods provide a p...
Peng Ding, Jennifer D. Key
STOC
2007
ACM
123views Algorithms» more  STOC 2007»
12 years 7 months ago
A 3-query PCP over integers
A classic result due to H?astad established that for every constant > 0, given an overdetermined system of linear equations over a finite field Fq where each equation depends o...
Venkatesan Guruswami, Prasad Raghavendra
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