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Results tagged with linear-independence
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user 83189
0
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Linear independence in $\mathbb{Z}_q^n$
Consider $\mathbb{Z}_q \equiv \mathbb{Z}/q\mathbb{Z}$, where $q \geqslant 2$. A set of vectors in $\mathbb{Z}_q^n$ is said to be linearly independent if no nontrivial linear combination of them produc …
- 503
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Does a random matrix over $\mathbb{Z}_q$ map linearly independent vectors to statistically i...
Suppose $A \in \mathbb{Z}_q^{n \times m}$ is a random $n \times m$ matrix whose entries are i.i.d. uniform over $\mathbb{Z}_q=\mathbb{Z}/q\mathbb{Z}$, where $q\geq2$. Let $\mathbf{x}_1, \ldots, \mathb …
- 503
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Maximum probability of a set of vectors from $ \mathbb{F}_2^n $ being linearly independent
Suppose $ m $ vectors from the vector space $ \mathbb{F}_2^n $ are selected independently according to a distribution $ P $ over $ \mathbb{F}_2^n $. Here $ \mathbb{F}_2 $ denotes the field with two el …
- 503