Examines erasure repair in augmented Reed-Muller codes, suggesting improved bandwidth efficiency over Reed-Solomon codes.
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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López et al. (2021) studied this question.
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