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All known results on covering radius are presented, as well as some new results. There are a number of upper and lower bounds, including asymptotic results, a few exact determinations of covering radius, some extensive relations with other aspects of coding theory through the Reed-Muller codes, and new results on the least covering radius of any linear [II,… (More)

Fuzzy sketches, introduced as a link between biometry and cryptography, are a way of handling biometric data matching as an error correction issue. We focus here on iris biometrics and look for the best error-correcting code in that respect. We show that two-dimensional iterative min-sum decoding leads to results near the theoretical limits. In particular,… (More)

ÐFault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset g of points in an undirected graph q
Y i is called an identifying code if the sets f
v g consisting of all elements of g within distance one from the vertex v are different. We also require that the sets f
v g are all nonempty. We take q to be… (More)

Let C be a code of length n over an alphabet of q letters. An n-word y is called a descendant of a set of t codewords x A code is said to have the t-identifying parent property if for any n-word that is a descendant of at most t parents it is possible to identify at least one of them. We prove that for any t ≤ q − 1 there exist sequences of such codes with… (More)

In an undirected graph G = (V; E) a subset C V is called an identifying code, if the sets B1 (v) \ C consisting of all elements of C within distance one from the vertex v are nonempty and diierent. We take G to be the innnite hexagonal grid, and show that the density of any identifying code is at least 16=39 and that there is an identifying code of density… (More)