Abstract
A k-server Private Information Retrieval (PIR) code is a binary linear [m, s]-code admitting a generator matrix such that for every integer i with \(1\le i\le s\) there exist k disjoint subsets of columns (called recovery sets) that add up to the vector of weight one, with the single 1 in position i. As shown in [8], a k-server PIR code is useful to reduce the storage overhead of a traditional k-server PIR protocol. Finding k-server PIR codes with a small blocklength for a given dimension has recently become an important research challenge. In this work, we propose new constructions of PIR codes from combinatorial structures, introducing the notion of k-partial packing. Several bounds over the existing literature are improved.
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Acknowledgments
This research was partially supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). The first author is funded by the project “Strutture Geometriche, Combinatoria e loro Applicazioni” (Fondo Ricerca di Base, 2019, University of Perugia). The third author is funded by the project “Metodi matematici per la firma digitale ed il cloud computing” (Programma Operativo Nazionale (PON) “Ricerca e Innovazione” 2014–2020, University of Perugia). The authors would like to thank Marco Buratti for his helpful suggestions.
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Giulietti, M., Sabatini, A., Timpanella, M. (2023). PIR Codes from Combinatorial Structures. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_10
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DOI: https://doi.org/10.1007/978-3-031-22944-2_10
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