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zbMATH Open
Article . 2018
Data sources: zbMATH Open
https://dx.doi.org/10.48550/ar...
Article . 2017
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
DBLP
Article
Data sources: DBLP
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Batch codes from Hamming and Reed-Muller codes

Authors: Travis BAUMBAUGH; Yariana DİAZ; Sophia FRİESENHAHN; Felice MANGANİELLO; Alexander VETTER;

Batch codes from Hamming and Reed-Muller codes

Abstract

Batch codes, introduced by Ishai et al., encode a string $x \in \Sigma^{k}$ into an $m$-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of $t$-users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. We look at locality and availability properties of first order Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than half their length.

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Keywords

batch codes, FOS: Computer and information sciences, 94B05, 94B60 (Primary), 94B65 (Secondary), Hamming codes, Reed-Muller codes, Batch codes;Hamming codes;Reed-Muller codes, Computer Science - Information Theory, Information Theory (cs.IT), Mühendislik, Engineering, recovery codes, Linear codes (general theory)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
gold