August 2011
Intermediate to advanced
332 pages
9h 10m
English
Content preview from Lattice Basis Reduction
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The LLL Algorithm 85
Exercise 4.16. Write a computer program (in a language other than Maple)
to implement the algorithm of Exercise 4.14. Test your program for various
values of α on the lattice consisting of all integral linear combinations of the
rows of the matrix X:
X =
8 8 7 5 1 2 6 0 6 3 1 4 5 9 3 4
5 7 8 3 2 2 1 5 5 3 5 3 9 2 7 0
4 9 0 3 0 9 6 5 9 4 5 9 2 6 8 2
1 4 6 5 4 1 2 7 5 2 7 9 8 9 9 9
3 8 1 3 6 5 2 9 3 4 4 6 1 4 0 5
6 1 1 5 1 4 1 7 5 2 0 7 6 2 8 2
2 5 5 1 1 5 7 0 5 0 6 3 9 7 8 1
1 7 3 3 8 6 4 3 8 4 4 6 4 1 8 4
Exercise 4.17. Modify the discussion of the closest vector problem in Section
4.4 so that the general reduction ...
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