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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“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”
—Blaise Pascal (1623–1662)
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The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)