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Geometrical Properties of Balls in Sum-Rank Metric (2303.11887v1)
Published 21 Mar 2023 in cs.IT and math.IT
Abstract: The sum-rank metric arises as an algebraic approach for coding in MIMO block-fading channels and multishot network coding. Codes designed in the sum-rank metric have raised interest in applications such as streaming codes, robust coded distributed storage systems and post-quantum secure cryptosystems. The sum-rank metric can be seen as a generalization of the well-known Hamming metric and the rank metric. As a relatively new metric, there are still many open theoretical problems for codes in the sum-rank metric. In this paper we investigate the geometrical properties of the balls with sum-rank radii motivated by investigating covering properties of codes.