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Dear Forum,

Raja Sekhar B <bachu@anise.ee.cornell.edu> writes:

Hi,

I wanted to know whether there exists a solution to this problem.

Let S be a subspace of a vector space over binary field F_2 of

dimension k. Let v be an element of s. Let w(v) = weight of v

defined as the number of ones in v. Is there a way

of finding the partition function for w ( i.e., finding

out how many vectors are there in S which have weight say j. This

turns out to be simple for the full space and happens to be

just the binomial expansion (k choose j)).

Hope someone answers fast

Thanks,

Raja

The command 'WeightDistribution' in the share package "guava" does

exactly what you want. For example,

gap> RequirePackage("guava"); gap> basis:=Z(2)* > [ [ 1, 0, 0, 0, 0, 1, 1 ], > [ 0, 1, 0, 0, 1, 0, 1 ], > [ 0, 0, 1, 0, 1, 1, 0 ], > [ 0, 0, 0, 1, 1, 1, 1 ] ] > ;; gap> C:=GeneratorMatCode(basis,GF(2)); # 4-dim subspace spanned by "basis". a linear [7,4,1..3]1 code defined by generator matrix over GF(2) gap> WeightDistribution(C); [ 1, 0, 0, 7, 7, 0, 0, 1 ]

This means that there is 1 vector each, of weight 0 and 7, and

that there are 7 vectors each, of weight 3 and 4.

Hope this helps,

Akihiro Munemasa

http://mac-mune.math.kyushu-u.ac.jp

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