PIR codes from combinatorial structures

07/02/2021

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by   Massimo Giulietti, et al.

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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≤ i≤ 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 <cit.>, 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.