• Because your $all_hash{ $n } = $m; is inside the for loop, you clobber the prior instance each time you reach a new one.
• Your variable names make your life more difficult
• As written, the value of your $n includes the &lt; (<) sign. Do you really want that?

The following may be what you're seeking:

#!/usr/bin/perl
use warnings;
use strict;
use 5.012;

# 902200

my @lines = qw(
    >seq1
    ASDFGHASDFGHJ
    ERTYUIOOIUYLK
    NBGFEWERTY
    >seq2
    BGTNHYMJUKOPK
    MNBFSDFGHJ
    >seq3
    USE_STRICT&USE_WARNINGS
    lastline
);


my $line;
my ($DNA, $seq);            # descriptive var names
my %all_hash = ();
for my $line (@lines){      # insert after this line, see update 2
        chomp $line;
        if ($line =~ /^>(seq\d)/ ) {  # captures seq# withOUT the '>'
                $seq = "$1\n";
             say "\n\$seq: $seq";  # useful for debug; otherwise, not
        } else {
            
                $DNA = "$line\n";
            say "\$DNA: $DNA";
        }
        no warnings;    #otherwise, warns 'unitialized' for the first 
+$DNA
        $all_hash{ $seq } .= $DNA;    # concat $DNAs, which now 
                                      # have '\n's restored for readab
+ility
        use warnings;
}

print "\n =============== \n";

print %all_hash;
[download]

Output (when fixed as per update 2):

$seq: seq1

$DNA: ASDFGHASDFGHJ

$DNA: ERTYUIOOIUYLK

$DNA: NBGFEWERTY


$seq: seq2

$DNA: BGTNHYMJUKOPK

$DNA: MNBFSDFGHJ


$seq: seq3

$DNA: USE_STRICT&USE_WARNINGS

$DNA: lastline


 ===============
seq1
ASDFGHASDFGHJ
ERTYUIOOIUYLK
NBGFEWERTY
seq3
USE_STRICT&USE_WARNINGS
lastline
seq2
BGTNHYMJUKOPK
MNBFSDFGHJ
[download]

Update

Added comment re say at line 29

Update2 : Missed a serious mistake here: the concat at line 36 actually inserts the last $DNA from the previous $seq into each new $seq. Bad on me! A fix is to reset $DNA to an empty string by inserting $DNA = ''; as a new line 26.

---

---

Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!

Titles consisting of a single word are discouraged, and in most cases are disallowed outright.

Read Where should I post X? if you're not absolutely sure you're posting in the right place.

Please read these before you post! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

Posts may use any of the Perl Monks Approved HTML tags:

a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr

You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

	For:		Use:
	&		&
	<		&lt;
	>		&gt;
	[		&#91;
	]		&#93;

Link using PerlMonks shortcuts! What shortcuts can I use for linking?

See Writeup Formatting Tips and other pages linked from there for more info.