= Ternary Hamming code as a negacyclic code
{title2=$C=\{c:c(\beta)=0\},\quad\operatorname{ord}(\beta)=3^s-1$}
Set $n=(3^s-1)/2$ and let $\beta$ be a <primitive element of a finite field> $\mathbb F_{3^s}$. The powers $1,\beta,\ldots,\beta^{n-1}$ represent every projective point once. Their <kernel> code is a <ternary Hamming code>. Since $\beta^n=-1$, its <polynomial> description is a <negacyclic code>, generated by the <minimal polynomial of an algebraic element> $\beta$ over $\mathbb F_3$.
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