Titlebook: List Decoding of Error-Correcting Codes; Winning Thesis of th Venkatesan Guruswami Book 2005 Springer-Verlag Berlin Heidelberg 2005 Code.Er

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10 List Decoding from ErasuresThe last two chapters presented a thorough investigation of the question of constructions of good codes, i.e. codes of high rate, which are list decodable from a very large, and essentially the “maximum” possible, fraction of errors.

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12 Sample Applications Outside Coding TheoryWe now move on to provide a sample of some of the applications which both combinatorial and algorithmic aspects of list decoding have found in contexts outside of coding theory. As it turns out, by now there are numerous such applications to complexity theory and cryptography.

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13 Concluding RemarksIn this work, we have addressed several fundamental questions concerning list decoding. We began in the first part with the study of certain combinatorial aspects of list decoding, and established lower and upper bounds on the number of errors correctable via list decoding, as a function of the rate and minimum distance of the code.

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https://doi.org/10.1007/b104335Code; Error-correcting Code; Information; Shannon; algorithms; coding theory; complexity theory; concatenat

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2 Preliminaries and Monograph Structure the fundamental code families and constructions that will be dealt with and used in this book. Finally, we discuss the structure of this work and the main results which are established in the technical chapters that follow, explaining in greater detail how the results of the various chapters fit together.

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5 List Decodability Vs. Ratereater than d/2). On the other hand, we have seen that, in general, the list decoding radius (for polynomial-sized lists), purely as a function of the distance of the code, cannot be larger than the Johnson radius.