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Results tagged with coding-theory
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user 16739
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".
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When can a binary matrix be transformed into a certain form
I have a $k \times n$ matrix $G$ over ${\mathbb F_2}$ that's full rank.
This can always be put in systematic form : $G \sim [I_k \mid P]$ where $I_k$ is a $k \times k$ identity matrix and $P$ is a $k …
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Effects of shortening and puncturing on codes
Given a binary block code $C=[n,k]$ of codeword length $n$, and dimension $k$.
Suppose I've determined these properties for it : $d_{min}$ (minimum distance),
$N_{dmin}$ (number of codewords at $d_{mi …
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