Upper Bounds on Matching Families in $\BBZ_{pq}^{n}$

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 Z
_m
ⁿ
, where Z
_m
is the ring of integers modulo m, is an interesting problem. In this paper, we show an upper bound of O ((pq)
^0.625n+0.125
) for the size of any matching family in Z
_pq
ⁿ
, 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 and coworkers.