Checking size of log file and taking backup

I want to check the size of a logfile and if it exceeds 10KB :

1)I need to move to  [logfile_time_pid.log]  .

2)Truncate  backup logfile (remove top lines until size of logfile is less than 10KB)

3)Write them back to backup logfile.

4)Create a fresh new logfile.

Here is the code I wrote:

my $MaxLogSize=10240 if ! $MaxLogSize;
if( -s "$LOGFILE" > $MaxLogSize ) {
    my $logbkp_name = time . "_" . $$; # backup logname
    my $OLD = $LOGFILE; # storing originial logname in a new variable
    $LOGFILE =~ s/\.log$/\_$logbkp_name\.log/; #substitute original log name with backuplog name
    rename($OLD,$LOGFILE); #move original file to backup file
    my @lines = qx(tail -c 10240 $LOGFILE); #get the 10KB size lines removing toplines
    open(OUT,">$LOGFILE") or die "$!\n"; #recreate backup file
    foreach (@lines)
    {
      print OUT $_ ; #write the lines to backup file
    }
    close(OUT);
    open(FH,">$OLD") or die "$!\n"; create a fresh original logfile
    }