Another tittle might be cyclic redundancy check or polynomial representation depending on the date of publication. Machine and biological functions both use Xor arithmetic logic which might seem a bit unusual, in particular:
1 = -1 (mod 2) or in words 2 is congruent to 0 (mod 2).
This will affect long division of polynomials that are to the base two, for example:
x2 + x2 = 0 and 0 – x = x.
A long division in Z2 is typically like so
(x6 + x4) ÷ (x4 + x3 + x2 + 0 + 1) = (x2 + x + 1) with a remainder of (x + 1)
We need to identify three of the four terms to encode the message.
(x4 + x3 + x2 + 0 + 1):Polynomial Generator p(x), 4th order.
(x6 + x4): Message (101) which was shifted 4 bits.
(x + 1) : Remainder which are check digits.
The code might be sent across the room or transmitted to the edge of the solar system. It is
x^6 + 0 + x^4 + 0 + 0 + x^1 + 1, or in binary
1010011
The code is divided by p(x); if the remainder is zero the code is valid.
Ape Town 