#20493: Rank of random matrices over GF(2) is bounded (again)
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Reporter: kedlaya | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.2
Component: linear algebra | Resolution:
Keywords: random matrices, rank, | Merged in:
pseudorandom numbers | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps: todo
Dependencies: |
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Comment (by kedlaya):
If I understand correctly how linear pseudorandom number generators work,
the Mersenne twister is computing iterates of a linear operator on
`F_2^19937` which acts as a permutation of this space, and the values we
see coming out of gmp are the result of applying some fixed linear
projection from `F_2^19937` to `F_2^32`. Since we're simply filling those
bits directly into the matrix, that limits the rank to 19937.
In order to break out of this, we need to do something nonlinear with the
gmp-provided bits...
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Ticket URL: <http://trac.sagemath.org/ticket/20493#comment:3>
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