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https://hdl.handle.net/10356/104524
Title: | Rank weight hierarchy of some classes of cyclic codes | Authors: | Ducoat, Jérôme Oggier, Frédérique |
Keywords: | DRNTU::Science::Physics::Atomic physics::Field theories | Issue Date: | 2014 | Source: | Ducoat, J., & Oggier, F. (2014). Rank weight hierarchy of some classes of cyclic codes. Proceedings of Information Theory Workshop (ITW), 2014 IEEE, 142-146. | Conference: | Information Theory Workshop (ITW), 2014 IEEE | Abstract: | 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. | URI: | https://hdl.handle.net/10356/104524 http://hdl.handle.net/10220/25585 |
DOI: | 10.1109/ITW.2014.6970809 | Schools: | School of Physical and Mathematical Sciences | Rights: | © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [http://dx.doi.org/10.1109/ITW.2014.6970809]. | Fulltext Permission: | open | Fulltext Availability: | With Fulltext |
Appears in Collections: | SPMS Conference Papers |
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