Rank weight hierarchy of some classes of cyclic codes

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, $m\ge 2$. 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.

Cited by in corpus (1)

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