Anticodes in the Sum-Rank Metric
Eimear Byrne, Heide Gluesing-Luerssen, Alberto Ravagnani
TL;DR
This paper provides a comprehensive classification of optimal linear anticodes in the sum-rank metric, compares their size to metric balls, and explores cases where largest anticodes are neither balls nor linear.
Contribution
It offers the first complete classification of optimal linear anticodes in the sum-rank metric for arbitrary fields and matrix sizes.
Findings
Optimal linear anticodes are fully classified.
The size of the largest anticodes exceeds that of metric balls over large finite fields.
Some largest anticodes are neither balls nor linear anticodes.
Abstract
We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsChromatin Remodeling and Cancer · Advanced MIMO Systems Optimization · Cooperative Communication and Network Coding