I just ran that example through the code I posted (Note: My code uses letters for columns not rows as you have). The groupings produced: 

23415
0000E
000BB


23415
AAAAA
CCC0C
DDD0D

[download]

gives rows 1 & 5 (your A & E), as a group which when subtracted from the remainer leaves rows 2, 3 & 4 (your {BCD}) as a group which is what you are after?

Full output from the unchanged program (except for inserting the new data (first line below)):

# my @grid = ( "AB0001","A0CD02","A0CD03","A0CD04","ABCDE5" );

c:\test>600418-2.pl
This input

        AB0001
        A0CD02
        A0CD03
        A0CD04
        ABCDE5
sorted

        A0CD02
        A0CD03
        A0CD04
        AB0001
        ABCDE5

Tranformed looks like this

        AAAAA
        000BB
        CCC0C
        DDD0D
        0000E
        23415
sorted

        0000E
        000BB
        23415
        AAAAA
        CCC0C
        DDD0D
These are the sets where the letters denote the columns of the origina
+l matrix
(0 mean column not used in this set).
And the numbers above, the rows they came from.

23415
0000E
000BB


23415
AAAAA
CCC0C
DDD0D

[download]
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
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In reply to Re^3: decomposing binary matrices by BrowserUk
in thread decomposing binary matrices by hv

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