Geometrical Properties of Balls in Sum-Rank Metric
Cornelia Ott, Hedongliang Liu, Antonia Wachter-Zeh
TL;DR
This paper explores the geometric properties of sum-rank metric balls, which are crucial for understanding code covering properties in applications like network coding and cryptography.
Contribution
It provides new insights into the geometry of sum-rank metric balls, addressing open theoretical problems in this emerging area.
Findings
Analysis of sum-rank metric ball structures
Implications for code covering properties
Foundations for future coding theory research
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.
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Liver Disease Diagnosis and Treatment