Mathematical Formulation
Let be a error-correcting code; in other words, is a code of length, dimension and minimum distance over an alphabet of size . The list-decoding problem can now be formulated as follows:
Input: Received word, error bound
Output: A list of all codewords whose hamming distance from is at most .
Read more about this topic: List Decoding
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“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
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The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)