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引用次数: 0
摘要
MRD码是在阶为q的有限域上m × n矩阵的秩距度量空间中的最大码。它们是直径完美的,如果m≥n,则具有基数q m (n−d +1)。我们将MRD码中的交换定义为用具有相同参数的其他子码替换特殊的MRD子码。我们考虑允许这种转换的MRD码的结构,包括刺穿扭曲加比都林码和直接产物码。使用切换,我们构造了一个巨大的MRD码类,当其他参数(n, q,码距)固定时,其基数在m中呈双指数增长。此外,我们还构造了不同仿射阶的MRD码和非周期MRD码。
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.