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EJC
2007
13 years 7 months ago
Binary codes from rectangular lattice graphs and permutation decoding
We examine the binary codes obtained from the row span over the field F2 of an adjacency matrix of the rectangular lattice graphs L2(m, n) for 3 ≤ m < n and show that permut...
Jennifer D. Key, P. Seneviratne
STOC
2006
ACM
130views Algorithms» more  STOC 2006»
14 years 8 months ago
Explicit capacity-achieving list-decodable codes
For every 0 < R < 1 and > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1 - R ...
Venkatesan Guruswami, Atri Rudra
TAMC
2007
Springer
14 years 1 months ago
On Deciding Deep Holes of Reed-Solomon Codes
For generalized Reed-Solomon codes, it has been proved [7] that the problem of determining if a received word is a deep hole is coNP-complete. The reduction relies on the fact that...
Qi Cheng, Elizabeth Murray
TIT
2010
136views Education» more  TIT 2010»
13 years 2 months ago
The existence of concatenated codes list-decodable up to the hamming bound
We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes ach...
Venkatesan Guruswami, Atri Rudra
TIT
2008
110views more  TIT 2008»
13 years 7 months ago
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every 0 < R...
Venkatesan Guruswami, Atri Rudra