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Science Forum Index » Cryptography Forum » Q: Space of substitutions
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| Mok-Kong Shen |
 Posted: Fri Dec 26, 2003 6:24 pm |
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Guest
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As is well-known, a vector space can have subspaces spanned
by a set of vectors of less number than the dimension of the
original vector space. Now consider the substitutions for
an alphabet of size n. Each substitution can be characterized
as a permutation of [0..n-1] and there are n! of these in
total. Suppose one chooses k (k << n!) of them and do all
compositions of up to s (s<=k) of these (duplicates allowed)
to obtain a set of permutations. It seems conceivable that
for certain choice of the k substitutions (that one starts
with) the size t of the resulting set will attain a maximum
value. The question is: What is the relation between t and
(k, s) and whether one could have an efficient algorithm to
find such an optimal set of k subsitutions for given (k, s).
[Apology, if the question turns out to be trivial.] Thanks
in advance.
M. K. Shen |
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