I explained in the
     initial presentation, where "+" is
     taken "modulo 2", or equivalently,
     in the "Galois Field of Order 2",
     GF(2).

JA:  A "field" is a mathematical system where you have
     things analogous to the usual "four operations" of
     addition, subtraction, multiplication, and division.

JA:  GF(2) consists of the set B = {0, 1} along with
     the following addition and multiplication tables:

|     + | 0 1
|     -------
|     0 | 0 1
|     1 | 1 0
|
|     . | 0 1
|     ----