[Tex/LaTex] XOR and II (concatenation) summation symbols

Question

In Latex, in math mode, if I want to express summation over a range I can use the following expression \sum_{from}^{to}. I can do the same for the product.

What is the name of the symbol that does this for XOR or concatenation?

If I do:

\oplus_{i=0}^7

I don't get the i=0 and 7 parts below and above the symbol, respectively, but to the right instead, like this:

With summation (\sum_{i=0}^7), that is not the case – they appear below and below in the output:

How can I make XOR, or concatenation (II) larger and with indices below and above the symbol?

Answer 1

You want to use \bigoplus instead of \oplus.

I've never seen concatenation done that way. Addition and XOR are commutative operations so it makes sense to sum over a set (or take the exclusive OR of a set). Concatenation is not like that. I think I would explicitly write out the concatenation. That said, you can use \bigparallel from the stmaryrd package.

\documentclass{article}
\usepackage{amsmath}
\usepackage{stmaryrd}
\newcommand*\concat{\mathbin{\|}}
\begin{document}
\[x_1\concat x_2\concat\dotsb\concat x_n\]
\[\bigparallel_{i=1}^n x_i\]
\end{document}