We study in graphs a property related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is a non-negative integer, if after the removal of any vertex no distance in the surviving graph increase by more than k. We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph. We also ...

The paper ‘‘Mean Distance and Minimum Degree,’’ by Mekkia Kouider and Peter Winkler, JGT 25#1 (1997), 95–99 mistakenly attributes the computer program GRAFFITI to Fajtlowitz and Waller, instead of just Fajtlowitz. (Our apologies to Siemion Fajtlowitz.) Note also that one of the ‘‘flaws’’ we note for Conjecture 62 (that it was made for graphs regular of degree d, vice graphs of minimum degree d)...

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With this in mind, we present a number of results on codes of minimum distance 2. We first compute the linear programming bound on the dimension of such a code, then...

A conjecture of Da Rocha concerning the minimum distance of a class of combinatorial codes is proven.

In this paper we introduce Symplectic Grassmann codes, in analogy to ordinary Grassmann codes and Orthogonal Grassmann codes, as projective codes defined by symplectic Grassmannians. Lagrangian–Grassmannian codes are a special class of Symplectic Grassmann codes. We describe all the parameters of line Symplectic Grassmann codes and we provide the full weight enumerator for the Lagrangian–Grassm...

In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods ...

In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph Γ, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of Γ is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that except for undirected cycles, any distance regular...

A binary nonlinear code can be represented as the union of cosets of a binary linear subcode. Using this representation, new algorithms methods to compute the minimum Hamming weight and distance are presented. The performance of these algorithms is also studied.

Many minimum distance estimators have the potential to provide parameter estimates which are both robust and efficient and yet, despite these highly desirable theoretical properties, they are rarely used in practice. This is because the performance of these estimators is rarely guaranteed per se but obtained by placing a suitable value on some tuning parameter. Hence there is a risk involved in...

In this paper we study the bidirectional shufjenet topology, which is obtained from the well-konwn (unidirectional) :huflenet by considering bidirectional knks. More specifically, we define a shortest-path routing algorithm, and derive the diameter and the average distance of the topology. The bidirectional shufjenet is then compared, in terms of average distance, with other variations of the p...