Efficiency considerations in using semi-random sources
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Private locally decodable codes
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
On the list decodability of random linear codes with large error rates
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Tree codes and a conjecture on exponential sums
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Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
Proceedings of the 5th conference on Innovations in theoretical computer science
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For any rateR, 0 < R < 1, a sequence of specific(n,k)binary codes with rateR_n > Rand minimum distancedis constructed such that begin{equation} lim_{n rightarrow infty} inf frac{d}{n} geq (1 - r ^{-1} R)H^{-1} (1 - r)> 0 end{equation} (and hence the codes are asymptotically good), whereris the maximum offrac{1}{2}and the solution of begin{equation} R = frac{r^2}{1 + log_2 [1 - H^{-1}(1 - r)]}. end{equation} The codes are extensions of the Reed-Solomon codes overGF(2^m)With a simple algebraic description of the added digits. Alternatively, the codes are the concatenation of a Reed-Solomon outer code of lengthN = 2^m - 1withNdistinct inner codes, namely all the codes in Wozeneraft's ensemble of randomly shifted codes. A decoding procedure is given that corrects all errors guaranteed correctable by the asymptotic lower bound ond. This procedure can be carried out by a simple decoder which performs approximatelyn^2 log ncomputations.