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From: "saeed kamelian" <kamelian.20@gmail.com>
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Subject: special matrix construction
Date: Tue, 19 Jul 2011 15:22:09 +0000 (UTC)
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Dear all

I want to construct a matrix with some special properties. i call this matrix G so the G matrix has the following properties
1-the G matrix's element are all 1 or 0
2-the G matrix always have bigger number of rows than columns or at least equal to the number of columns  (#rows>=#columns)
3-sum of all of elements of G(sum of all 1's) is equal to number of rows
4-sum of all elements in each row of G is equal to 1
5-there is at least one 1 in each column of G matrix.
I want to have and list all of the possible case of G matrix with that stated properties.
for example if we have 4 rows and 2 columns the all possible G matrix are like below:
0 1      1 0     1 0      1 0
1 0      0 1     1 0      1 0
1 0      1 0     0 1      1 0 
1 0      1 0     1 0      0 1
(1)      (2)      (3)       (4)
0 1    0 1       0 1     1 0    1 0     1 0
0 1    1 0       1 0     0 1    0 1     1 0
1 0    0 1       1 0     0 1    1 0     0 1
1 0    1 0       0 1     1 0    0 1     0 1
(5)    (6)        (7)     (8)    (9)    (10)

0 1    0 1    0 1       1 0 
0 1    0 1    1 0       0 1
0 1    1 0    0 1       0 1
1 0    0 1    0 1       0 1
(11)   (12)  (13)     (14)

these are all 14 possible case when number of rows is 4 and number of column is 2
how can i write a code for arbitrary number of rows and columns.

i think total number of possible case can be calculated from the following formula
m= number of rows
n= number of columns

n^m - ( n * (n-1)^m )

m=4
n=2
2^4 - (2*(2-1)^4))=14

regards