Improved bounds for dictionary look-up with one error

Given a dictionary S of n binary strings each of length m, we consider the problem of designing a data structure for S that supports d-queries; given a binary query string q of length m, a d-query reports if there exists a string in S within Hamming distance d of q. We construct a data structure for the case d = 1, that requires space O(n log m) and has query time O(1) in a cell probe model with word size m. This generalizes and improves the previous bounds of Yao and Yao for the problem in the bit probe model.