تقرير
Constructing MRD codes by switching
| العنوان: | Constructing MRD codes by switching |
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| المؤلفون: | Shi, Minjia, Krotov, Denis S., Özbudak, Ferruh |
| المصدر: | J. Comb. Des. 32(5) 2024, 219-237 |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Information Theory, Computer Science - Discrete Mathematics, Mathematics - Combinatorics, 94B25 |
| الوصف: | MRD codes are maximum codes in the rank-distance metric space on $m$-by-$n$ matrices over the finite field of order $q$. They are diameter perfect and have the cardinality $q^{m(n-d+1)}$ if $m\ge n$. We define switching in MRD codes as replacing special MRD subcodes by other subcodes with the same parameters. We consider constructions of MRD codes admitting such switching, including 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. Keywords: MRD codes, rank distance, bilinear forms graph, switching, diameter perfect codes |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1002/jcd.21931 |
| URL الوصول: | http://arxiv.org/abs/2211.00298 |
| رقم الأكسشن: | edsarx.2211.00298 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1002/jcd.21931 |
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