Results 261 to 270 of about 51,101 (296)

The Covering Radius of a Mapping and the Multiplicity of a Covering

Siberian Mathematical Journal, 2001
The article is a continuation of the author's study of a geometrical characteristic of a mapping from \(\mathbb R^n\) into \(\mathbb R^n\) [\textit{V.~I.~Semenov}, Sib. Math. J. 40, No. 4, 793-800 (1998); translation from Sib. Mat. Zh. 40, No. 4, 938-946 (1999; Zbl 0932.30018)], wherein, for a continuous a.e.
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The Covering Radius of the Leech Lattice

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1982
Abstract We investigate the points in 24-dimensional space at maximum distance from the Leech lattice, i. e. the ‘deepest holes’ in that lattice. The maximum distance of any such point from the Leech lattice is shown to be 1/√2 times the minimum distance between the lattice points. Furthermore there are 23 types of ‘deepest hole’, one
Conway, J. H., Parker, R. A., Sloane, N. J. A.   +2 more
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Packing radius, covering radius, and dual distance

IEEE Transactions on Information Theory, 1995
Recently, A. Tietäväinen derived an upper bound on the covering radius of codes as a function of the dual distance. This was generalized to the minimum distance, and to \(Q\)-polynomial association schemes by Levenshtein and Fazakas. Both proofs use a linear programming approach.
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Subcodes and covering radius

IEEE Trans. Inf. Theory, 1986
A sharp lower bound on the covering radius of a linear, binary code is given in terms of the covering radius of any subcode of index two. An upper bound on the norm of a code is then derived. These results hold for all linear codes over GF(2).
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On the covering radius of convolutional codes

1994
We consider a problem of calculating covering capabilities for convolutional codes. An upper bound on covering radius for convolutional code is obtained by random coding arguments. The estimates on covering radius for some codes with small constraint length are presented.
Irina E. Bocharova, Boris D. Kudryashov
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On Covering Radius and Discrete Chebyshev Polynomials

Applicable Algebra in Engineering, Communication and Computing, 1997
The authors show that using discrete Chebyshev polynomials instead of regular ones they get an improvement on the Honkala-Litsyn-Tietäväinen bound. In a certain interval this new bound is also better than Tietäväinen's bound. Upper bounds on even-weight codes are considered as well.
Iiro S. Honkala, Tero Laihonen, Simon Litsyn   +2 more
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Bounds on the Covering Radius of Linear Codes

Designs, Codes and Cryptography, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexei E. Ashikhmin, Alexander Barg
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On the multi-radius cover problem

Information Processing Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Multi-radius Cover Problem

2005
Let G = (V,E) be a graph with a non-negative edge length lu,v for every (u,v) ∈ E. The vertices of G represent locations at which transmission stations are positioned, and each edge of G represents a continuum of demand points to which we should transmit.
Refael Hassin, Danny Segev
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Covering radius---Survey and recent results

IEEE Transactions on Information Theory, 1985
All known results on the covering radius are presented, as well as some new results. Lower and upper bounds on covering radius are given in sections II and III, respectively. Section IV gives covering radius results for Reed-Muller codes, and section V deals with the least covering radius of \((n,k)\) codes.
Gérard D. Cohen, Mark G. Karpovsky, H. F. Mattson Jr., James R. Schatz   +3 more
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