Department of Mathematics - Seminar on Pure Mathematics - Generalized Covering Radii of Reed–Muller Codes

In this talk, we study generalized covering radii, a fundamental property of linear codes that captures the trade-off between storage, latency, and access complexity in linear data-query protocols such as private information retrieval (PIR). We introduce several equivalent definitions, highlighting the combinatorial, geometric, and algebraic perspectives of this notion. We then derive lower and upper bounds on the generalized covering radii of Reed–Muller codes and determine their exact values in certain extreme cases.