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Parvaresh–Vardy codes are a family of error-correcting codes first described in 2005 by Farzad Parvaresh and Alexander Vardy. [1] They can be used for efficient list-decoding . See also
A code has all-symbol locality and availability if every code symbol can be recovered from disjoint repair sets of other symbols, each set of size at most symbols. Such codes are called ( r , t ) a {\displaystyle (r,t)_{a}} -LRC.
Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
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The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.
Lawson-Perfect's approach is to represent each part of a question as a function of the answer to the previous part. That is, if a student answer's "x" for part a, the correct answer to part b is "f(x)." No matter what the student puts for part a, the corresponding answer for part b can be calculated quickly.
An error-correcting code is a way of encoding x as a message such that Bob will successfully understand the value x as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received.
One of the most famous error-correcting codes, the Hadamard code, is a locally testable code. A codeword x is encoded in the Hadamard code to be the linear function () = (mod 2). This requires listing out the result of this function for every possible y, which requires exponentially more bits than its input.