Uncoverings on graphs and network reliability

We propose a network protocol similar to the $k$-tree protocol of Itai and Rodeh [{\em Inform.\ and Comput.}\ {\bf 79} (1988), 43--59]. To do this, we define an {\em $t$-uncovering-by-bases} for a connected graph $G$ to be a collection $\mathcal{U}$ of spanning trees for $G$ such that any $t$-subset of edges of $G$ is disjoint from at least one tree in $\mathcal{U}$, where $t$ is some integer strictly less than the edge connectivity of $G$. We construct examples of these for some infinite families of graphs. Many of these infinite families utilise factorisations or decompositions of graphs. In every case the size of the uncovering-by-bases is no larger than the number of edges in the graph and we conjecture that this may be true in general.Comment: 12 pages, 5 figure

Permutation codes

AbstractThere are many analogies between subsets and permutations of a set, and in particular between sets of subsets and sets of permutations. The theories share many features, but there are also big differences. This paper is a survey of old and new results about sets (and groups) of permutations, concentrating on the analogies and on the relations to coding theory. Several open problems are described

Error-Correcting codes fromk-resolving sets

We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the k-metric dimension of grid graphs (i.e., Cartesian products of paths)

A McEliece cryptosystem using permutation codes

This paper is an attempt to build a new public-key cryptosystem; similar to the McEliece cryptosystem, using permutation error-correcting codes. We study a public-key cryptosystem built using two permutation error-correcting codes. We show that these cryptosystems are insecure. However, the general framework in these cryptosystems can use any permutation error-correcting code and is interesting

Decoding generalised hyperoctahedral groups and asymptotic analysis of correctible error patterns

We demonstrate a majority-logic decoding algorithm for decoding the generalised hyperoctahedral group $C_m \wr S_n$ when thought of as an error-correcting code. We also find the complexity of this decoding algorithm and compare it with that of another, more general, algorithm. Finally, we enumerate the number of error patterns exceeding the correction capability that can be successfully decoded by this algorithm, and analyse this asymptotically

Three moments of audience address in 20th century artistic production

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1991.Includes bibliographical references (leaves 141-148).This paper examines strategies of audience address as manifest in the work of the Russian avant-garde of the 1920s, the sculptural practices of the American Minimalists and the critics who served to define their endeavors, as well as the more recent projects of institutional critique that have characterized one trajectory of post-minimalist artistic production. Vladimir Tatlin and EI Lissitzky attempted to meet the demands of a newly-forming proletariat class by siting their work in the space of political and public activity. This effort to engender a simultaneous collective response, a notion theorized by Walter Benjamin, was unsuccessful: Lissitzky returned, instead, to the space of exhibition, the conventional arena of artistic discourse, where he designed a series of exhibition rooms that created an active spectator and made visible the ordering systems of the institution. Seen in light of these radical precedents, Minimalism and its critics appear to have been caught in an approach whose departure point was the physical and phenomenological nature of the object and its context-a retreat from the path initiated by Lissitzky. With the arrival of conceptual art some fifty years later, the late Constructivist explorations would re-emerge as the practice of institutional critique. These latter modes of artistic production have examined the socio-political and economic underpinnings of the institution, the composition of its audiences, and the modes of art viewing that it has promoted.by Abigail Deser.M.S