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Results tagged with coding-theory
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user 2294
The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".
4
votes
How to find the $\pm 1$ vector that is closest to a given vector $(r_1, \dots, r_l)$? Is it ...
Let the $R_i$ be $\pm 1$ vectors and the $V_i$ be a linear space over GF(2). This then becomes the problem of maximum likelihood decoding of binary linear codes, which is known to be an NP-hard proble …
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4
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Large subgroups of the Hamming cube
You can get half of the elements small. Let $e_k$ be the element $(0,0,\ldots,0,1,0, \ldots 0)$ with a single $1$ in the $k$th position. Let $v$ be the element $(1,1,1,1,1,\ldots,1)$. Now, consider th …
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