Analysis

Inequality of complex numbers ★★

Author(s):

Conjecture   There exists a real positive $ c $, such that for any $ n\in\mathbb{N} $ and any $ z_i\in\mathbb{C} $ where $ |z_i|\le 1 $ for $ 1\le i\le n $ and $ \~z:=\frac{1}{n}\sum^n_{k=1}z_k $, the following holds: $$\left|\prod^n_{k=1}z_k - \~z^n\right| \le c\cdot\sum^n_{k=1}|z_k-\~z|^2$$

Keywords:

Posted by feanor
updated January 5th, 2011
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Combinatorics » Codes

Perfect 2-error-correcting codes over arbitrary finite alphabets. ★★

Author(s):

Conjecture   Does there exist a nontrivial perfect 2-error-correcting code over any finite alphabet, other than the ternary Golay code?

Keywords: 2-error-correcting; code; existence; perfect; perfect code

Posted by davidcullen
updated April 3rd, 2010
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