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 do… Show more
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