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Roos bound for skew cyclic codes in Hamming and rank metric


Alfarano, Gianira Nicoletta; Lobillo, F J; Neri, Alessandro (2021). Roos bound for skew cyclic codes in Hamming and rank metric. Finite Fields and Their Applications, 69:101772.

Abstract

In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a general field is provided. The result holds in the Hamming metric and in the rank metric. The proofs involve arithmetic properties of skew polynomials and an analysis of the rank of parity-check matrices. For the rank metric case, a way to arithmetically construct codes with a prescribed minimum rank distance, using the skew Roos bound, is also given. Moreover, some examples of MDS codes and MRD codes over finite fields are built, using the skew Roos bound.

Abstract

In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a general field is provided. The result holds in the Hamming metric and in the rank metric. The proofs involve arithmetic properties of skew polynomials and an analysis of the rank of parity-check matrices. For the rank metric case, a way to arithmetically construct codes with a prescribed minimum rank distance, using the skew Roos bound, is also given. Moreover, some examples of MDS codes and MRD codes over finite fields are built, using the skew Roos bound.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Theoretical Computer Science
Physical Sciences > Algebra and Number Theory
Physical Sciences > General Engineering
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Theoretical Computer Science, General Engineering, Algebra and Number Theory, Applied Mathematics
Language:English
Date:1 January 2021
Deposited On:10 Aug 2021 15:49
Last Modified:25 Apr 2024 01:38
Publisher:Elsevier
ISSN:1071-5797
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.ffa.2020.101772
Project Information:
  • : FunderSNSF
  • : Grant ID200021_188430
  • : Project TitleNew Constructions of Convolutional Codes
  • : FunderSNSF
  • : Grant IDP2ZHP2_187711
  • : Project TitleAlgebraic Methods for Rank-Metric Codes in Post-Quantum Cryptography and Communications
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)