All Questions
Tagged with it.information-theory ag.algebraic-geometry
8 questions
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From a constraint satisfaction problem (CSP) to a sudoku grid [closed]
one of the existing methods of solvin a sudoku grid is via constraints satisfaction (CSP), but can we do the inverse ie convert a CSP problem into a sudoku grid and then solve it ?
2
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45
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Moduli spaces of 'generalized mutually unbiased bases'
Mutually unbiased bases in $\mathbb{C}^n$ with a chosen inner product are collections of orthonormal bases such that for each pair of orthonormal bases $e_i,f_i$, $i=1,\ldots,n$ we have $|\langle e_i, ...
- 7,633
2
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142
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List decodability of Reed-Solomon codes beyond the Johnson bound
In a paper on a proximity test for Reed-Solomon codes the authors state an "extremely optimistical" conjecture on the list decodability of Reed-Solomon codes (over prime fields $\mathbb F_q$)...
- 81
4
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1
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Polynomial time decodable binary linear codes achieving $GV$ bound?
Are there explicit or random construction of linear codes that achieve the $GV$ bound with polynomial time decodable property with alphabet size $q=2$?
Tsfasman, Manin, Vladut beat the bound at ...
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- 1
4
votes
1
answer
638
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Stability in algebraic geometry
Suppose I have a collection of polynomials with multiple variables (more polynomials than variables, say), and I'm given noisy versions the values of these polynomials at a certain unknown point. I ...
- 148k
7
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2
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Are algebraic geometry error correcting codes (Goppa codes) "good" ?
Question (informal version): Are algebraic geometry error correcting codes (V.D. Goppa codes) "good" ?
Some details. There is certain construction of error-correcting codes by means of algebraic ...
- 13.9k
3
votes
1
answer
531
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How many vectors of Hamming weight L in "random" K dimensional subspace of F_2^N ? Or how good/bad is random linear block code ?
Consider linear $N$-dimensional space $F_2^N$.
Consider its $K$ dimensional subspace $V \subset F_2^N$.
Let us calculate $w(k,V,N)$ number of vectors in $V$ of Hamming weight $k$ in $V$.
Since there ...
- 24.9k
0
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1
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262
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Number of points on a complex sphere with pairwise inner product restriction
Considered the following inner products:
$(1)$ $\langle x,y \rangle = \sum_{t=1}^{n}x_{t}y_{t}$
$(2)$ $\langle x,y \rangle_{c} = \sum_{t=1}^{n}x_{t}\bar{y}_{t}$
consider the following surfaces:
$\...
- 13.9k