How to manipulate some fields using Views PHP?
You'll want to put that code into a view template. Go into your admin, where you can edit that View, click on Advanced, and then Theme: Information. That will give you suggestions on the file naming conventions for the row style output for your view.

But as for your PHP code, Drupal uses a lot of nested multi-dimensional arrays, so it's not as simple as $row-&gt;field_authors being an array of strings of author names (unless you're doing some preprocessing). If field_authors is a term reference, you'll need to load the taxonomy term in order to get the actual author name.

This should get you the $names array:

$names = [];
foreach($row-&gt;field_field_authors as $author_tid){
   $term = taxonomy_term_load($author_tid[0]['tid']);
   $names[] = $term-&gt;name;
}
(... the rest of your code...)