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TIT
2010
111views Education» more  TIT 2010»
13 years 6 months ago
On correctable errors of binary linear codes
The error correction capability of binary linear codes with minimum distance decoding, in particular the number of correctable/uncorrectable errors, is investigated for general lin...
Kenji Yasunaga, Toru Fujiwara
PROPERTYTESTING
2010
13 years 10 months ago
Some Recent Results on Local Testing of Sparse Linear Codes
We study the local testability of linear codes. We first reformulate this question in the language of tolerant linearity testing under a non-uniform distribution. We then study th...
Swastik Kopparty, Shubhangi Saraf
TIT
2002
129views more  TIT 2002»
13 years 11 months ago
Combinatorial bounds for list decoding
Abstract--Informally, an error-correcting code has "nice" listdecodability properties if every Hamming ball of "large" radius has a "small" number of ...
Venkatesan Guruswami, Johan Håstad, Madhu Su...
DAM
1998
88views more  DAM 1998»
13 years 11 months ago
Neither Reading Few Bits Twice Nor Reading Illegally Helps Much
We first consider so-called (1,+s)-branching programs in which along every consistent path at most s variables are tested more than once. We prove that any such program computing...
Stasys Jukna, Alexander A. Razborov
TIT
2008
83views more  TIT 2008»
13 years 12 months ago
Hard Problems of Algebraic Geometry Codes
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic proble...
Qi Cheng
TIT
2008
103views more  TIT 2008»
13 years 12 months ago
Improved Probabilistic Bounds on Stopping Redundancy
For a linear code , the stopping redundancy of is defined as the minimum number of check nodes in a Tanner graph T for such that the size of the smallest stopping set in T is equal...
Junsheng Han, Paul H. Siegel, Alexander Vardy
DM
2007
112views more  DM 2007»
13 years 12 months ago
Affine blocking sets, three-dimensional codes and the Griesmer bound
We construct families of three-dimensional linear codes that attain the Griesmer bound and give a probablistic construction of linear codes that are close to the Griesmer bound. Al...
Simeon Ball, Elisa Montanucci
CORR
2007
Springer
132views Education» more  CORR 2007»
13 years 12 months ago
Matroid Pathwidth and Code Trellis Complexity
We relate the notion of matroid pathwidth to the minimum trellis state-complexity (which we term trellis-width) of a linear code, and to the pathwidth of a graph. By reducing from ...
Navin Kashyap
CORR
2006
Springer
92views Education» more  CORR 2006»
14 years 9 hour ago
Highly robust error correction by convex programming
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x Rn (a block of n pieces of information) to a remote receiver. We ask wh...
Emmanuel J. Candès, Paige A. Randall
INFOCOM
2002
IEEE
14 years 4 months ago
Beyond Routing: An Algebraic Approach to Network Coding
Abstract— In this paper we consider the issue of network capacity. The recent work by Li and Yeung examined the network capacity of multicast networks and related capacity to cut...
Muriel Médard, Ralf Koetter