Upper Bounds on Matching Families in
Yeow Meng Chee, San Ling, Huaxiong Wang, Liang Feng Zhang · 2013
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.