Locally testable and Locally correctable Codes Approaching the Gilbert-Varshamov Bound

IEEE Trans. Information Theory, Volume 64, Issue 8, 2018, Pages 5813-5831.

Cited by: 13|Views76
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Abstract:

One of the most important open problems in the theory of error-correcting codes is to determine the tradeoff between the rate R and minimum distance δ of a binary code. The best known tradeoff is the Gilbert-Varshamov bound, and says that for every δ ∈ (0, 1/2), there are codes with minimum distance δ and rate R = RGV (δ) > 0 (for a certa...More

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