Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon

polyhedral representation of a code polytope is first presented. We show how these results can be extended to obtain the complete facial structure of the polytope determined by the [n, n−1] even-weight code. We then give a result classifying the types of 3-faces a general code polytope can have, which shows

and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational

] in the course of studying stream ciphers. In this work we develop techniques for finding the multicovering radius of specific codes. In particular, we study the even weight code, the 2-error correcting BCH code, and linear codes with covering radius one. We also study questions involving the complexity

list gives all examples of cometric association schemes known to us (see [15] for details on spherical designs): • Q-polynomial distance-regular graphs (this includes all symmetric 2-class schemes); • duals of metric translation schemes (e.g, the subscheme induced on even-weight code

For any q which is a power of 2 we describe a finite subgroup of GLqðCÞ under which the complete weight enumerators of generalized doubly-even self-dual codes over Fq are invariant. An explicit description of the invariant ring and some applications to extremality of such codes are obtained

Relations between the local weight distributions of a binary linear code, its extended code, and its even weight subcode are presented. In particular, for a code of which the extended code is transitive invariant and contains only codewords with weight multiples of four, the local weight

of the contribution of interferences from all other nodes, weighted by a coefficient gamma, and of a background noise. We find that there is a critical value of gamma above which the network is made of disconnected clusters of nodes. We also prove that if gamma is non zero but small enough, there exist node spatial

Abstract—This work provides techniques to apply the channel coding theorem and the resulting error exponent, which was originally derived for totally random block-code ensembles, to ensembles of codes with less restrictive randomness demands. As an example, the random coding technique can even

de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury: