Rank weight hierarchy of some classes of cyclic codes
Date of Issue2014
Information Theory Workshop (ITW), 2014 IEEE
School of Physical and Mathematical Sciences
We study the rank weight hierarchy, thus in particular the rank metric, of cyclic codes over the finite field Fqm, q a prime power, m ≤ 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(Fq) 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.
DRNTU::Science::Physics::Atomic physics::Field theories
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