Constructing MRD codes by switching Full article
| Journal |
Journal of Combinatorial Designs
ISSN: 1063-8539 |
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| Output data | Year: 2024, Volume: 32, Number: 5, Pages: 219-237 Pages count : 19 DOI: 10.1002/jcd.21931 | ||||||
| Tags | MRD codes, rank distance, bilinear forms graph, switching | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
Maximum rank-distance (MRD) codes are (not necessarily linear) maximum codes in the rank-distance metric space on $m$-by-$n$ matrices over a finite field GF$(q)$. They are diameter perfect and have the cardinality $q^{m(n-d+1)}$ if $m\ge n$. We define switching in MRD codes as the replacement of special MRD subcodes by other subcodes with the same parameters. We consider constructions of MRD codes admitting switching, such as punctured twisted Gabidulin codes and direct-product codes. Using switching, we construct a huge class of MRD codes whose cardinality grows doubly exponentially in $m$ if the other parameters ($n$, $q$, the code distance) are fixed. Moreover, we construct MRD codes with different affine ranks and aperiodic MRD codes.
Cite:
Shi M.
, Krotov D.S.
, Özbudak F.
Constructing MRD codes by switching
Journal of Combinatorial Designs. 2024. V.32. N5. P.219-237. DOI: 10.1002/jcd.21931 WOS Scopus РИНЦ OpenAlex
Constructing MRD codes by switching
Journal of Combinatorial Designs. 2024. V.32. N5. P.219-237. DOI: 10.1002/jcd.21931 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Sep 11, 2022 |
| Accepted: | Dec 30, 2023 |
| Published print: | Feb 8, 2024 |
| Published online: | Feb 8, 2024 |
Identifiers:
| Web of science: | WOS:001157772900001 |
| Scopus: | 2-s2.0-85184696353 |
| Elibrary: | 66122011 |
| OpenAlex: | W4391656897 |