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Codes Endowed With the Rank Metric (1710.02067v1)
Published 5 Oct 2017 in cs.IT, math.CO, and math.IT
Abstract: We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix representation. We then investigate the combinatorial structure of MRD codes and optimal anticodes in the rank metric, describing how they relate to each other.