In this article, we introduce a new and simple data structure, the prefix table under Hamming distance, and present two algorithms to compute it efficiently: one asymptotically fast; the other very fast on average and in practice. Because the latter approach avoids the computation of global data structures, such as the suffix array and the longest common prefix array, it yields algorithms much ...

It is proved that codes of length n, covering radius Z?, and minimum Hamming distance 2R-1 are normal if R does not divide n. Constructions for abnormal codes with covering radius R and minimum Hamming distance at least R-l are given.

iv Acknowledgments v Chapter

Let [n, k, d]q -codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, the nonexistence of [105, 6, 68]3 and [230, 6, 152]3 codes is proved. © 2004 Elsevier B.V. All rights reserved.

We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1−`, n+`], where 1 ≤ ` ≤ n+1, by flipping a single bit in each step. This is a far-ranging generalization of the wellknown middle two levels problem (the case ` = 1). We provide a solution for the case ` = 2 and solve a relaxed version of the problem for general valu...

We survey recent results on a few distance labelling problems for hypercubes and Hamming graphs.