Geometrical Properties of Balls in Sum-Rank Metric
Konferenz: WSA & SCC 2023 - 26th International ITG Workshop on Smart Antennas and 13th Conference on Systems, Communications, and Coding
27.02.2023–03.03.2023 in Braunschweig, Germany
Tagungsband: ITG-Fb. 308: WSA & SCC 2023
Seiten: 6Sprache: EnglischTyp: PDF
Autoren:
Ott, Cornelia (Institute of Communications Engineering, Ulm University, Germany)
Liu, Hedongliang; Wachter-Zeh, Antonia (Institute for Communications Engineering, Technical University of Munich (TUM), Germany)
Inhalt:
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.