ApCoCoALib:RingF16

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ApCoCoALib contains an implementation of the field $\mathbb {F} _{16}$ The field is constructed via $\mathbb {F} _{16}=\mathbb {F} [x]/(x^{4}+x^{3}+1)$. The field's elements are represented as integers between 0 and 15. The corresponding mapping is the substitution homomorphism, mapping x to 2. Therefore we have e.g. $x^{3}+x+1\mapsto 2^{3}+2^{1}+2^{0}=8+2+1=11$. A more detailed description of this behavior can be found in the article ApCoCoA:Representation_of_finite_fields.

This implementation is contained in the files RingF16,[CH]. A new instance can be created with the command:

ApCoCoA::AlgebraicCore::NewRingF16();

An example, describing how to use RingF16, especially together with ring homomorphisms can be found in ApCoCoALib's example directory. It is named ex-RingF16.C