24 research outputs found
Optimal Ferrers Diagram Rank-Metric Codes
Optimal rank-metric codes in Ferrers diagrams are considered. Such codes
consist of matrices having zeros at certain fixed positions and can be used to
construct good codes in the projective space. Four techniques and constructions
of Ferrers diagram rank-metric codes are presented, each providing optimal
codes for different diagrams and parameters.Comment: to be presented in Algebra, Codes, and Networks, Bordeaux, June 16 -
20, 201
Bounds for the multilevel construction
One of the main problems in random network coding is to compute good lower
and upper bounds on the achievable cardinality of the so-called subspace codes
in the projective space for a given minimum distance. The
determination of the exact maximum cardinality is a very tough discrete
optimization problem involving a huge number of symmetries. Besides some
explicit constructions for \textit{good} subspace codes several of the most
success full constructions involve the solution of discrete optimization
subproblems itself, which mostly have not been not been solved systematically.
Here we consider the multilevel a.k.a.\ Echelon--Ferrers construction and given
lower and upper bounds for the achievable cardinalities. From a more general
point of view, we solve maximum clique problems in weighted graphs, where the
weights can be polynomials in the field size .Comment: 95 page