Given a dictionary

of

binary strings each of length

, we consider the problem of designing a data structure for

that
supports

-
queries; given a binary query string

of length

, a

-query reports if there exists a string in

within Hamming distance

of

. We construct a data structure for the case

, that requires space

and has query time

in a cell probe model with word size

. This generalizes and improves the previous bounds of Yao and Yao for the
problem in the bit probe model