62,481 research outputs found
On the similarities between generalized rank and Hamming weights and their applications to network coding
Rank weights and generalized rank weights have been proven to characterize
error and erasure correction, and information leakage in linear network coding,
in the same way as Hamming weights and generalized Hamming weights describe
classical error and erasure correction, and information leakage in wire-tap
channels of type II and code-based secret sharing. Although many similarities
between both cases have been established and proven in the literature, many
other known results in the Hamming case, such as bounds or characterizations of
weight-preserving maps, have not been translated to the rank case yet, or in
some cases have been proven after developing a different machinery. The aim of
this paper is to further relate both weights and generalized weights, show that
the results and proofs in both cases are usually essentially the same, and see
the significance of these similarities in network coding. Some of the new
results in the rank case also have new consequences in the Hamming case
KMS weights on higher rank buildings
We extend some of the results of Carey-Marcolli-Rennie on modular index
invariants of Mumford curves to the case of higher rank buildings: we discuss
notions of KMS weights on buildings, that generalize the construction of graph
weights over graph C*-algebras.Comment: 25 pages, LaTeX, 4 jpg figure
Multivariate data analysis: The French way
This paper presents exploratory techniques for multivariate data, many of
them well known to French statisticians and ecologists, but few well understood
in North American culture. We present the general framework of duality diagrams
which encompasses discriminant analysis, correspondence analysis and principal
components, and we show how this framework can be generalized to the regression
of graphs on covariates.Comment: Published in at http://dx.doi.org/10.1214/193940307000000455 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
We restrict a degenerate quadratic form over a finite field of odd
characteristic to subspaces. Thus, a quotient space related to is
introduced. Then we get a non-degenerate quadratic form induced by over the
quotient space. Some related results on the subspaces and quotient space are
obtained. Based on this, we solve the weight hierarchies of a family of linear
codes related to Comment: 12 page
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