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Results tagged with coding-theory
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user 36577
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".
6
votes
1
answer
160
views
Characterization of metrics such that the volume of balls doesn't depend on their centers?
Given a finite metric space $(X,d)$,
when does it hold that for all $y\in X$ and $r>0$, $\#B(y,r)$ does not depend on $y$?
Here $ B(y,r):=\{x\in X: d(x,y)\le r\} $ denotes a ball of radius $r$ centere …
- 161
7
votes
2
answers
430
views
How to count the number of tensors over a finite field of tensor rank $r$?
For simplicity, work over $\mathbb F_2$ and only consider order-$3$ equilateral tensors. For $r\in\mathbb Z_{>0}$, how many tensors $\mathfrak{T}\in\mathsf{Ten}_{n}^{\otimes 3}(\mathbb F_2)$ are there …
- 161