8.3 THE ALGEBRA OF POLYNOMIALS OVER 
will denote the set of polynomials in the variable z whose coefficients {pi} are in
:
Arithmetic operations on polynomials are the usual, except that the addition and multiplication of coefficients is performed modulo 2. We write deg(p) for the degree of p ∈ The subset of
consisting of polynomials with deg(p) ≤ n will be denoted by Pn[z]. We next summarize several basic properties of
.
8.3.1 Properties of 
- f ∈
has a factorization, if f(z) = g(z)h(z) with g, h ∈ . If f(z) = g(z)h(z), then g(z) and h(z) are factors of f(z)
(a) f(z) = g(z)h(z) is a non-trivial ...
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