On the idempotents of cyclic codes over $\mathbb{F}_{2^t}$
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Abstract
We study cyclic codes of length $n$ over $\mathbb{F}_{2^t}$. Cyclic codes can be viewed as ideals in $\mathcal{R}_n = \mathbb{F}_{2^t}[x]/(x^n - 1)$. It is known that there is a unique generating idempotent for each ideal. Let $e(x) \in \mathcal{R}_n$. If $t = 1$ or $t = 2$, then there is a necessary and sufficient condition that $e(x)$ is an idempotent. But there is no known similar result for $t \geq 3$. In this paper we give an answer for this problem.
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References
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