Around Reed-Muller codes
Linear Algebra seminar by Alexander Barg, University of Maryland
Hosted by Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University
Monday 10:05 New York (GMT-4)
Recording available
Abstract
Alexander Barg explores research questions inspired by Reed–Muller codes. The first concerns storage codes on triangle-free graphs, where neighboring vertices determine parity checks. Certain graphs admit codes approaching the maximum size of 2^n; whether Reed–Muller codes yield similar constructions remains open. The second extends the construction of Reed–Muller codes from cosets in an elementary abelian group to Coxeter groups, including permutation groups. Questions include analogues of the |u|u+v| construction and modern decoders, whether these codes share Reed–Muller codes' capacity achievement on the binary erasure channel, and a conjectured minimum-distance formula.