2021•Unpublished venueRequires access

Augmented Reed-Muller Codes of High Rate and Erasure Repair

Hiram H. López, Gretchen L. Matthews, Daniel Valvo

Abstract

We present two families of augmented Reed-Muller (ARM) codes, which are evaluation codes obtained by adding specific vectors to a Reed-Muller code. We develop exact repair schemes for single erasures for these ARM codes. When a dimension and a base field are fixed, we give examples where ARM codes provide a lower bandwidth in comparison with Reed-Solomon codes. We analyze the asymptotical behavior when ARM codes achieve the maximum rate.

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Key concepts: Reed–Solomon error correction, Reed–Muller code, Tornado code, Erasure code, Raptor code, Computer science, Luby transform code, Online codes