In this paper, we give lower and upper bounds on the covering radius of codes over the ring Z4 with respect to chinese euclidean distance. We also determine the covering radius of various Repetition codes, Simplex codes Type α and Type β and give bounds on the covering radius for MacDonald codes of both types over Z4.

The results of this paper are concerned with the multi-covering radius, a generalization of covering radius, of Rank Distance (RD) codes. This leads to greater understanding of RD codes and their distance properties. Results on multi-covering radii of RD codes under various constructions are given by varying the parameters. Some bounds are established. A relationship between multi-covering radi...

We study the covering radius of sets of permutations with respect to the Hamming distance. Let f(n, s) be the smallest number m for which there is a set of m permutations in Sn with covering radius r ≤ n − s. We study f(n, s) in the general case and also in the case when the set of permutations forms a group. We find f(n, 1) exactly and bounds on f(n, s) for s > 1. For s = 2 our bounds are line...

In this paper, we restudy the covering radius of block codes from an information theoretic point of view by ignoring the combinatorial formulation of the problem. In the new setting, the formula of the statistically defined minimum covering radius, for which the probability mass of uncovered space by M spheres can be made arbitrarily small, is reduced to a minimization of a statistically define...

Designing a good error-correcting code is a packing problem. The corresponding covering problem has received much less attention: now the codewords must be placed so that no vector of the space is very far from the nearest codeword. The two problems are quite different, and with a few exceptions good packings, i.e. codes with a large minimal distance, are usually not especially good coverings. ...

In the face of budgetary limitations in organizations, identifying critical facilities for investing in quality improvement plans could be a sensible approach. In this paper, hierarchical facilities with specified covering radius are considered. If disruption happens to a facility, its covering radius will be decreased. For this problem, a bi-objective mathematical formulation is proposed. Crit...

In this paper, we give lower and upper bounds on the covering radius of codes over the ring R = Z2 + uZ2, where u2 = 0 with bachoc distance and also obtain the covering radius of various Repetition codes, Simplex codes of α-Type code and β-Type code. We give bounds on the covering radius for MacDonald codes of both types over R = Z2 + uZ2. MSC: 20C05, 20C07, 94A05, 94A24.

The covering radius problem is a question in coding theory concerned with finding the minimum radius r such that, given a code that is a subset of an underlying metric space, balls of radius r over its code words cover the entire metric space. Klapper ([13]) introduced a code parameter, called the multicovering radius, which is a generalization of the covering radius. In this paper, we introduc...

In 1981, Schatz proved that the covering radius of the binary ReedMuller code RM(2, 6) is 18. For RM(2, 7), we only know that its covering radius is between 40 and 44. In this paper, we prove that the covering radius of the binary Reed-Muller code RM(2, 7) is at most 42. Moreover, we give a sufficient and necessary condition for Boolean functions of 7-variable to achieve the second-order nonlin...

We study covering codes of permutations with the l∞-metric. We provide a general code construction, which uses smaller building-block codes. We study cyclic transitive groups as building blocks, determining their exact covering radius, and showing linear-time algorithms for finding a covering codeword. We also bound the covering radius of relabeled cyclic transitive groups under conjugation. In...