= Check polynomial of a cyclic code
{title2=$h(X)=(X^N-1)/g(X)$}
= Check polynomials of a cyclic code
{synonym}
For a cyclic code with monic generator $g\mid X^N-1$, the canonical check polynomial is $h=(X^N-1)/g$. A word $a$ belongs to the code exactly when $ah$ is zero modulo $X^N-1$, since cancellation in the polynomial ring turns this condition into $g\mid a$. The kernel condition alone allows additional polynomials: it is equivalent to $\gcd(\widetilde h,X^N-1)=h$. Requiring the monic divisor of the modulus singles out the canonical choice.
// Target: algebra.bigb
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