Binary codes with XOR operation forms an abelian group.
\( \displaystyle (\{T,F\},\oplus ) \) or \( \langle B^n, \bigoplus \rangle \) is an abelian group.
- associativity : \( (a \oplus b) \oplus c = a \oplus (b \oplus c) \)
- identity element : \( 0 \oplus a = a \)
- \( a \oplus a = 0 \) every element is its own inverse
- commutativity : \( a \oplus b = b \oplus a \)
binary words: strings of 1s and 0s.
the set of all binary words of length n called \( B^n \)