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Title: Rank weight hierarchy of some classes of polynomial codes
Authors: Ducoat, Jérôme
Oggier, Frédérique
Keywords: Science::Mathematics
Issue Date: 2022
Source: Ducoat, J. & Oggier, F. (2022). Rank weight hierarchy of some classes of polynomial codes. Designs, Codes and Cryptography.
Project: NRF-RF2009-07
Journal: Designs, Codes and Cryptography
Abstract: We study the rank weight hierarchy, thus in particular the minimum rank distance, of polynomial codes over the finite field $\FF_{q^m}$, $q$ a prime power, $m \geq 2$. We assume that polynomials involved are squarefree. We establish the rank weight hierarchy of $[n,n-1]$ constacyclic codes. We characterize polynomial codes of $r$th rank weight $r$, and in particular of irst rank or minimum rank distance 1. Finally, we provide a refinement of the Singleton bound, from which we show that cyclic codes cannot be MRD (maximum rank distance) codes, but constacyclic codes can be.
ISSN: 0925-1022
DOI: 10.1007/s10623-022-01181-6
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. All rights reserved. This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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