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Multiplication

The field multiplication determines the operation

$$\star: [\![0,2^n-1]\!]\times[\![0,2^n-1]\!]\to [\![0,2^n-1]\!... ...h $\delta$}}) \mapsto I_{\mbox{\scriptsize\boldmath $\gamma$}},$$

where the vector index $\mbox{\boldmath$\gamma$}$ is such that $p_{\mbox{\scriptsize\boldmath$\gamma$}}(X)=p_{\mbox{\scriptsize\boldmath$\epsilon$}}(X) p_{\mbox{\scriptsize\boldmath$\delta$}}(X)$. In tables 7-11 these operations are displayed for $n=2,3,4,5$ respectively.

Table: Multiplication table in the Galois field $\mathbb{F}_{2^2}$.

(a)	(b)

Table: Multiplication table in the Galois field $\mathbb{F}_{2^3}$.

(a)	(b)

Table: Multiplication table in the Galois field $\mathbb{F}_{2^4}$.

(a)

(b)

Table: Multiplication table in the Galois field $\mathbb{F}_{2^5}$ (numeric values).

Table: Multiplication table in the Galois field $\mathbb{F}_{2^5}$ (density plot).

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