Roos bound for skew cyclic codes in Hamming and rank metric
| Autor: | Gianira N. Alfarano, Alessandro Neri, Francisco Javier Lobillo |
|---|---|
| Přispěvatelé: | University of Zurich, Alfarano, Gianira Nicoletta |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Rank (linear algebra) Computer Science - Information Theory Field (mathematics) 0102 computer and information sciences Mathematical proof 01 natural sciences Theoretical Computer Science Combinatorics 510 Mathematics 2604 Applied Mathematics 0101 mathematics 2614 Theoretical Computer Science Mathematics Algebra and Number Theory 11T71 94B65 16S36 Information Theory (cs.IT) Applied Mathematics 010102 general mathematics Skew General Engineering Hamming distance ddc 10123 Institute of Mathematics Finite field 010201 computation theory & mathematics Metric (mathematics) 2200 General Engineering Hamming code 2602 Algebra and Number Theory |
| Popis: | 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. Comment: 15 pages |
| Databáze: | OpenAIRE |
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