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**1 - 5**of**5**### Complexity of error-correcting codes

"... derived from combinatorial games \Lambda ..."

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### Connecting Identifying Codes and Fundamental Bounds

, 2011

"... We consider the problem of generating a connected robust identifying code of a graph, by which we mean a subgraph with two properties: (i) it is connected, (ii) it is robust identifying, in the sense that the (subgraph-) induced neighborhoods of any two vertices differ by at least 2r + 1 vertices, ..."

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We consider the problem of generating a connected robust identifying code of a graph, by which we mean a subgraph with two properties: (i) it is connected, (ii) it is robust identifying, in the sense that the (subgraph-) induced neighborhoods of any two vertices differ by at least 2r + 1 vertices, where r is the robustness parameter. This particular formulation builds upon a rich literature on the identifying code problem but adds a property that is important for some practical networking applications. We concretely show that this modified problem is NP-complete and provide an otherwise efficient algorithm for computing it for an arbitrary graph. We demonstrate a connection between the the sizes of certain connected identifying codes and errorcorrecting code of a given distance. One consequence of this is that robustness leads to connectivity of identifying codes.

### Covering Radius Construction Codes With Minimum Distance At Most 8 Are Normal

, 2003

"... In this paper we introduce the class of covering radius (CR)-codes as a generalization of greedy codes. First we show how a CR-code is constructed and introduce some basic terminology. Some properties which are satisfied by these codes are then discussed. We review the property of normality for code ..."

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In this paper we introduce the class of covering radius (CR)-codes as a generalization of greedy codes. First we show how a CR-code is constructed and introduce some basic terminology. Some properties which are satisfied by these codes are then discussed. We review the property of normality for codes and show that CR-codes with minimum distance at most 8 are normal. 1

### IMPLEMENTING THE LEXICOGRAPHIC CONSTRUCTION By

, 2006

"... Lexicographic construction is a greedy algorithm that produces error correcting codes known as lexicodes. The most surprising fact about lexicodes is that they possess some distinctive characteristics, contrary to the first impression that they do not have any interesting structure. In this project ..."

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Lexicographic construction is a greedy algorithm that produces error correcting codes known as lexicodes. The most surprising fact about lexicodes is that they possess some distinctive characteristics, contrary to the first impression that they do not have any interesting structure. In this project we observe these distinctive characteristics of the lexicodes in order to produce the optimal algorithm for the current technology level.