Upper Bounds on Matching Families in $\mathbb{Z}_{pq}^n$

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 Zm, where Zm is the ring of integers modulo m, is an interesting problem. In this paper, we show an upper bound of O((pq)) for the size of any matching family in Zpq , where p and q are two distinct primes. Our bound is valid when n is a constant, p → ∞ and p/q → 1. Our result improves an upper bound of Dvir et al.