Notation: Meaning of brackets with subscript?

Question

I came across the following expression: $[m + 2r + 2\sum_{i \in S}{x_i}]_{x_0}$. What does the subscripted bracket notation mean?

Context: Found in this paper https://eprint.iacr.org/2009/616.pdf. Page 6, Section 3.1, in description of "Encrypt" function.

Answer 1

In section 2, the paper gives this definition: