Abstract
Linear batch codes and codes for private information retrieval (PIR) with a query size t and a restricted size r of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of t or r by providing corresponding constructions. By building on the ideas of Cadambe and Mazumdar, a new bound in a recursive form is derived for batch codes and PIR codes.
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Acknowledgment
The work of E. Thomas and V. Skachek is supported by the Estonian Research Council under the grants PUT405 and IUT2-1. The authors wish to thank Mart Simisker for valuable comments on the earliest version of this work.
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Thomas, E.K., Skachek, V. (2017). Constructions and Bounds for Batch Codes with Small Parameters. In: Barbero, Á., Skachek, V., Ytrehus, Ø. (eds) Coding Theory and Applications. ICMCTA 2017. Lecture Notes in Computer Science(), vol 10495. Springer, Cham. https://doi.org/10.1007/978-3-319-66278-7_24
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DOI: https://doi.org/10.1007/978-3-319-66278-7_24
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