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arXiv · 1407.3962

Rank weight hierarchy of some classes of cyclic codes

Jérôme Ducoat·Frédérique Oggier
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Abstract

We study the rank weight hierarchy, thus in particular the rank metric, of cyclic codes over the finite field $\mathbb F_{q^m}$, $q$ a prime power, $m \geq 2$. We establish the rank weight hierarchy for $[n,n-1]$ cyclic codes and characterize $[n,k]$ cyclic codes of rank metric 1 when (1) $k=1$, (2) $n$ and $q$ are coprime, and (3) the characteristic $char(\mathbb F_q)$ divides $n$. Finally, for $n$ and $q$ coprime, cyclic codes of minimal $r$-rank are characterized, and a refinement of the Singleton bound for the rank weight is derived.

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Jérôme Ducoat, Frédérique Oggier. 2014-07-15. Rank weight hierarchy of some classes of cyclic codes. https://arxiv.org/abs/1407.3962

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