Hi
my first hints:
a) use 'use strict;' to protect yourself. Yes, this advice is annoying but helpful.
b) The script gives warnings on runtime: Follow them.
c) The line for ($j = 1; $j <= 20;$j++) is IMHO wrong as a perl array is accessed with index starting with 0, so for ($j = 0; $j < 20;$j++).
d) Why do you use an external program to generate random numbers? See perldoc -f rand.
e) Don't initialize the random numer generator before every rand().
f) Your code to instantiate the %nuc-hash is in a way that you get an array of strings. Afterwards you convert them implicitly to float numbers. So instantiate them acordingly.

%nuc = (
'F' => [0.001, 0.001, ...],
...
)
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g) Instead of programming this "ugly" if-elsif-else-statement at the end use a mapping-hash. It's better readable, it's better maintainable and it's less error prone.

my %mapping = (
    1 => "A",
    2 => "R",
    3 => "N",
    ...
);
if(exists $mapping{$names[$j]}) {
    $names[$j] = $mapping{$names[$j]};
}
else {
    # Default value (last else-Statement)
    $names[$j]="V";
}
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