I can not repeat your problem on my system with 5.10.0. The message points to the correct line:

$ cat foo.pl
my $state = 0;
print "state = $state\n";
$state = 1;
print "state = $state\n";
$state = 4;
print "state = $state\n";
state = 5;
print "state = $state\n";
$
$ perl -Mstrict foo.pl
Can't modify constant item in scalar assignment at foo.pl line 7, near
+ "5;"
Bareword "state" not allowed while "strict subs" in use at foo.pl line
+ 7.
Execution of foo.pl aborted due to compilation errors.
$
$ perl -v

This is perl, v5.10.0 built for x86_64-linux

Copyright 1987-2007, Larry Wall

Perl may be copied only under the terms of either the Artistic License
+ or the
GNU General Public License, which may be found in the Perl 5 source ki
+t.

Complete documentation for Perl, including FAQ lists, should be found 
+on
this system using "man perl" or "perldoc perl".  If you have access to
+ the
Internet, point your browser at http://www.perl.org/, the Perl Home Pa
+ge.

$
[download]

I also tried Perl versions 5.8.8 and 5.12.0.