Linear batch codes and codes for private information retrieval (PIR) with a query size @math and a restricted size @math of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of @math or of @math 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.
In this paper, we study a construction of binary switch codes. A switch code is a code such that a multi-set request of information symbols can be simultaneously recovered from disjoint sets of codeword symbols. Our construction is optimal in the sense that it has the smallest codeword length given its average encoding degree, which is logarithmic in the code dimension. Moreover, the number of queries needed to recover any information symbol in the request is at most 2. As a result, our construction is the first family of switch codes with low encoding and decoding complexity.