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Results tagged with coding-theory
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user 23827
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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Maximum of the weighted binomial sum $2^{-r}\sum_{i=0}^r\binom{m}{i}$
Let $m$ be a positive integer and let $f_m(r)=2^{-r}\sum_{i=0}^r\binom{m}{i}$. Clearly $f_m(0)=f_m(m)=1$ and $f_{2r+1}(r)=2^{2r}$.
Conjecture: If $m>12$, then the maximum value of $f_m(r)$ for $r\in\{ …
- 1,991