If your code is truly going to be the slug (“secret-page” = example.com/secret-page), you could do something like this…
wp_redirect(get_bloginfo('url')."https://wordpress.stackexchange.com/".$_POST['access_code']);
But realize that headers cannot have already been sent, so this needs to happen before get_header(). Some more testing would be needed, but that should get you down the right path in principle.
You could also have the form’s action be "https://wordpress.stackexchange.com/", method as $_GET and make the name of the input be "name" (<input name="name" ...>).
So if you visit
example.com/?name=my-secret-page
you will end up at
example.com/my-secret-page
as that is default behavior when using “pretty” permalinks