Abstract. Locally decodable codes are error correcting codes that simultaneously provide efficient random-access to encoded data and high noise resilience by allowing reliable reconstruction of an arbitrary data bit from looking at only a small number of randomly chosen codeword bits. Local decodability comes at the price of certain loss in terms of code efficiency. Specifically, locally decodable codes require longer codeword lengths than their classical counterparts. In this work we briefly survey the recent progress in constructions of locally decodable codes. 1

Matching families are one of the major ingredients in the construction of locally decodable codes (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in, where is the ring of inte-gers modulo, is an interesting problem. In this paper, we show an upper bound of for the size of anymatching family in, where and are two distinct primes. Our bound is valid when is a constant, , and. Our result improves an upper bound of Dvir and coworkers.