{"title":"Constructing MRD codes by switching","authors":"M. Shi, D. Krotov, F. Özbudak","doi":"10.48550/arXiv.2211.00298","DOIUrl":null,"url":null,"abstract":"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 ≥ 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.","PeriodicalId":14826,"journal":{"name":"Journal of Acupuncture and Tuina Science","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Acupuncture and Tuina Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2211.00298","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"INTEGRATIVE & COMPLEMENTARY MEDICINE","Score":null,"Total":0}
引用次数: 0
Abstract
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 ≥ 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.
期刊介绍:
Journal of Acupuncture and Tuina Science (ISSN 1672-3597, CN 31-1908/R) is a journal with an international scope, focusing on the popularization of traditional Chinese medicine and acupuncture- moxibustion culture, the promotion of international exchanges and the prosperity of clinical Chinese medicine and acupuncture-moxibustion. Journal of Acupuncture and Tuina Science mainly involves clinical practice and emphasizes the presentation of the detailed methods of observing and treating clinical common diseases on which acupuncture-moxibustion has a good effect. The articles are characterized by practicality, briefness and reproducibility. The main contents include the experiences of senior TCM doctors, forum on special diseases, clinical reports, brief reports, education series, terminology and brief introduction to new books. Communications regarding Academy activities are also appropriate.