
On qary codes with two distances d and d+1
The qary block codes with two distances d and d+1 are considered. Sever...
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Lifted codes and the multilevel construction for constant dimension codes
Constant dimension codes are e.g. used for error correction and detectio...
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Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances
We employ signed measures that are positive definite up to certain degre...
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On three domination numbers in block graphs
The problems of determining minimum identifying, locatingdominating or ...
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The interplay of different metrics for the construction of constant dimension codes
A basic problem for constant dimension codes is to determine the maximum...
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Subspace exploration: Bounds on Projected Frequency Estimation
Given an n Γ d dimensional dataset A, a projection query specifies a sub...
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Multilevel constructions: coding, packing and geometric uniformity
Lattice and special nonlattice multilevel constellations constructed fro...
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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 socalled subspace codes in the projective space π«_q(n) 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 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. EchelonβFerrers 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 q.
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