Improved Gilbert–Varshamov Bound for Sum-Rank-Metric Codes via Graph Theory

IEEE Transactions on Information Theory 2026 Open access

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Authors: Aida Abiad, Harper Reijnders, Michael B. Tait
DOI: 10.1109/tit.2026.3691929
Cited by: 0

Abstract

We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that asymptotically Fn×mqcan be partitioned into sum-rank-metric codes whose average size is bigger than the GV bound by a logarithmic factor for these parameters. Finally, we discuss the connection of such codes to set-coloring Ramsey numbers.

Fields of Study & Subjects

graph theory and CDMA systems Graph Labeling and Dimension Problems Complexity and Algorithms in Graphs

Publication details

Journal / source
IEEE Transactions on Information Theory
Volume
72
Issue
7
Pages
4828–4836
Publication date
11 May 2026
Language
EN