The LaTeX command for bigoplus (⊕) is \bigoplus.
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Write \bigoplus inside math mode, that is between $…$ for inline math or in a \[ … \] or equation block for display math. It is part of core LaTeX math, so no extra package is required.
\bigoplus is a math-mode symbol: in running text, wrap it in $...$. With unicode-math under XeLaTeX or LuaLaTeX, typing ⊕ in a formula gives the same symbol.
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x'x''\angle\measuredangle\triangle\diamond\bigodot\bigotimes\mathcal{L}\mathcal{H}\mathcal{F}\mathcal{A}\mathcal{B}\mathcal{C}More math symbols in LaTeX: the full table or search all 350+ LaTeX symbols.
Use \bigoplus in math mode; it needs no extra package. For example, $\bigoplus$.
None: \bigoplus is built into LaTeX, so no extra package is required.