In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2-th parts, for i ∈ {1, . . . , u} of binary (respectively, extended binary) Hamming codes of length n = 2 − 1 (respectively, 2), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs...

The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem of constructing optimal ternary constant-composition codes with Hamming weight four and minimum distance six. The problem is solved with a small number of len...

Let Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance, and En (respectively, On) the set of vectors with even (respectively, odd) weight. For r 1 and x 2 Fn, we denote by Br(x) the ball of radius r and centre x. A code C Fn is said to be r-identifying if the sets Br(x)\C, x 2 Fn, are all nonempty and distinct. A code C En is said to be r-discrimi...

Given a language L, the Hamming distance of a string x to L is the minimum Hamming distance of x to any string in L. The edit distance of a string to a given language is deened similarly. First, we prove that the Hamming distance to languages in AC 0 is hard to approximate; it cannot be approximated within a factor O ? n 1 3 ? , for any > 0, unless P = NP (n denotes the length of the input stri...

In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight of the codes parameterized by the edges of any complete bipartite graph. Also, at the beginning, we obtain some results about the generalized Hamming weights of some evaluation codes arising from a complete intersect...