In mycode.pl, put an END block that creates a file to show the job has been completed, have your "master" script submit the jobs, then periodically check if *all* the files are available before concatinating.

# in mycode.pl
END {
 system("touch done$param");
};

# in master.pl
SLEEPY:
while (1) 
{
    sleep(5);
    for my $done (@done_list)
    {
        next SLEEPY if ! -e $done;
    };
    last;
};
# cat files now:
etc..
[download]