In this article, we determine the minimum distance of the Euclidean dual of the cyclic code $\mathcal{ C}_n$ generated by the $n$th cyclotomic polynomial $Q_n(x)$ over $\mathbb{ F}_q$, for every positive integer $n$ co-prime to $q$. In particular, we prove that the minimum distance of $\mathcal{ C}_{ n}^{ \perp}$ is a function of $n$, namely $2^{ \omega(n)}$. This was precisely the conjecture posed by us in \cite{ BHAGAT2025}.
Categories: cs.IT math.IT