More on fields and polynomial

Have just learned that:

F_{2}=Z_{2}=\left\{ \bar{0},\bar{1}\right\}

F_{4}=\left\{\left(a,b: a,b \epsilon F_{2}\right) \right\} means that the elements are

\left(\bar{0},\bar{0} \right) , \left(\bar{0},\bar{1} \right) , \left(\bar{1},\bar{0} \right) and \left(\bar{1},\bar{1} \right)

F_{8}=F_{2^{3}}\left\{\left(a, b, c: a, b, c \epsilon F_{2} \right) \right\}

F_{2^{n}} means that we’ll have n tuple, thus we’ll have a polynomial with n degree

(degree is the highest exponent of the polynomial).

Example:

\left(\bar{1}, \bar{0}, \bar{1}, \bar{1} \right) means x^{3}+x+1

Important notes:

F_{p}=Z_{p} is only if p is prime. F_{8}\neq Z_{8}

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