1. Remove the newlines between two related statements
2. Align the closing curly braces to the same column where their opening counterpart is
3. Don't do all the date calculation manually. Use Date::Simple or Date::Calc instead.

After that you script will be much shorter and better readable, and you can start to think about enhancements.

Can't load modules on target host.

#!/usr/bin/perl
use strict;

# THIS SCRIPT CONCATENATES DATA FOR 1 WEEK OF RELIANT TRUST DATA AND S
+ENDS TO NDM
#
my $MAIL_ALIAS='my.email.com'; # Mail Alias used for sending emails
my $ASL='app-server'; # what the heck is ASL?????????!!!!
my @LOG_FILENAMES=('name1.log','name2.log');


my($yyyy,$mm,$dd) = deduct_date_values( timestamp_days_back(1) );
my $abs_log_yesterday = "$0.$dd.log";


sub secsday { return (3600 * 24) } # to give you an idea how far you c
+ould consider breaking this up

sub deduct_date_values {
   my $timestamp = shift;
   $timestamp or die; # expect the 'impossible'

   require Time::Format;
   my $date_string = Time::Format::time_format('yyyy_mm_dd',$timestamp
+);

   my($yyyy,$mm,$dd) = split( /_/, $date_string );

   # make sure
   $yyyy or die;
   $mm or die;
   $dd or die;

   return ($yyyy,$mm,$dd);
}

sub timestamp_days_back {
   my $numdays = shift;
   $numdays or die;
   my $then = ( time - ( $numdays * secsday() ) );
   return $then;
}


if ($yesterwday == 5) {

    # compute last 7 days of file names

    # cat the files

    foreach $logfilename (@LOG_FILENAMES) {

        my $abs_cat_target = "$logfilename.$year$mm$dd";


        unlink $abs_cat_target;   # in case we run 2x in one day 

        for my $i (5,6,7,8) {

            for my $days_back (7,6,5,4,3,2,1) {       # Number of days
+ to go back for process

                my($yyyy,$mm,$dd) = deduct_date_values( timestamp_days
+_back($days_back) );             
                my $abs_file = "$logfilename.myservername$i\.$year$mm$
+dd";

                
                $command = "cat $fileext.$ASL$i >> $catfile 2>/dev/nul
+l";

                if ($debug) {

                    print "WOULD $command\n";

                } else {

                    $output = `$command`;

                }
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Now, some serious pointers. Things you may think trivial but are actually make or break. Label your scalars/symbols descriptively. Don't use shotcuts like 'f' to mean absolute path to logfile , call it $absolute_path_to_logfile

Use strict. Don't play russian roulette with this. Maybe the data you are handling is actually valuable information.

Do what the pros tell you to do.
The more time passes, the more I come to agree with the higher monks. Try out what they suggest, understand it, then reject it if you still want to- after you've done it, used it.

There's a *reason* for the anal retentiveness of things like using strict and naming variables properly- and it's not to make our life harder or to patronize the noobs.
It's to make your life better and easier.

If you ignore people telling you to use strict- and you continue using perl, you will be using strict. It will just take longer to come around- and slow down your learning curve. I think that to learn to do as much as you did, you must have been exposed to 'use strict' a lot of times. Believe it. Don't doubt it.

I hope this is not going too far up your ***. I would have cleaned out your script but I have to tell you my friend, it's impossible unless I'm you- because of how the code is written.
I would let most of this go for a noob. But from looking at your code, I *know* you're new to perl but not to computers. You know some shiznit. You need a peer to smack you upside the head- here it is.

If you see yourself using perl in the future, you need Damian Conway's Perl Best Practices, you can get it for $5 at amazon.com.

and you can start to think about enhancements.

Like encapsulating the @cmd construction and processing into a sub.

#!/usr/bin/perl -w
or
#!/usr/bin/perl
use warnings;

My objective here is to: 1) Clean this script up

#!/usr/bin/perl
use warnings;
use strict;

# THIS SCRIPT CONCATENATES DATA FOR 1 WEEK OF RELIANT TRUST DATA AND S
+ENDS TO NDM
#
my $MT  = 'my.email.com';                 # Mail Alias used for sendin
+g emails
my $ASL = 'app-server';
my @BFL = qw( name1.log name2.log );

# START TIME AND DATE VARIABLES
#
my ( $mday, $mon, $year, $wday ) = ( localtime $^T - 3600 * 24 )[ 3 ..
+ 6 ];

# Saturday only
exit 0 if $wday != 5;
#
#   END TIME AND DATE VARIABLES

for my $f ( @BFL ) {
    my $catfile = sprintf '%s.%d%02d%02d', $f, $year + 1900, $mon + 1,
+ $mday;

    open my $CAT, '>', $catfile or die "Cannot open '$catfile' $!";

    for my $i ( 5 .. 8 ) {
        for my $dd ( reverse 1 .. 7 ) {    # Number of days to go back
+ for process
            my ( $mday, $mon, $year ) = ( localtime $^T - $dd * 3600 *
+ 24 )[ 3 .. 5 ];

            my $fileext = sprintf '%s.myservername%d.%d%02d%02d', $f, 
+$i, $year + 1900, $mon + 1, $mday;

            open my $IN, '<', "$fileext.$ASL$i" or warn "Cannot open '
+$fileext.$ASL$i' $!";

            print $CAT while <$IN>;
            }
        }

    # the cat-ed file is produced: scp it
    my $filetoput = "/home/echxfr/$catfile";
    my @cmd = ( '/usr/bin/scp', $catfile, "cduser\@ndm:$filetoput", );

    my $rv = system @cmd;
    if ( $rv == -1 ) {
        print "Unable to execute scp: $!\n";
        }
    elsif ( $rv & 127 ) {
        printf "scp to died with signal %d\n", $rv & 127;
        }
    elsif ( $rv >> 8 ) {
        printf "scp exited with error %d\n", $rv >> 8;
        }
    else {
        print "scp was successful\n";
        }

    if ( -z $catfile ) {
        0 == system '/bin/mailx', '-s', "ERROR: Reliant SCP Log file $
+catfile sent to ndm is empty", $MT
            or warn "system 'mailx' failed: $?";
        }
    }
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