See "Why it's stupid to 'use a variable as a variable name'" - Part 1, Part 2, Part 3.

There are good reasons why use strict makes symbolic references (aka "using variables as variable names") illegal. It's a really bad idea.

In your case, I can't see any advantage that you have over just using an array called @ARR (though a better naming strategy might be nice). In the general case, you're almost always better off using hashes to store references to arrays.