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Randomized and explicit constructions of linear error-correcting codes enable efficient encoding and decoding.
We present a new class of asymptotically good, linear error-correcting codes. These codes can be both encoded and decoded in linear time. They can also be encoded by logarithmic-depth circuits of linear size and decoded by logarithmic depth circuits of size O(nlogn). We present both randomized and explicit constructions of these codes.
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Daniel A. Spielman (1996) studied this question.
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