Results 271 to 280 of about 87,508 (304)
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IEEE Transactions on Information Theory, 2006
Summary: A code \(C\subseteq \mathbb Z_n^2\), where \(\mathbb Z^2=\{0,1\}\), has unidirectional covering radius \(R\) if \(R\) is the smallest integer so that any word in \(\mathbb Z_n^2\) can be obtained from at least one codeword \(c\in C\) by replacing either 1's by 0's in at most \(R\) coordinates or 0's by 1's in at most \(R\) coordinates.
Patric R. J. Östergård +1 more
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Summary: A code \(C\subseteq \mathbb Z_n^2\), where \(\mathbb Z^2=\{0,1\}\), has unidirectional covering radius \(R\) if \(R\) is the smallest integer so that any word in \(\mathbb Z_n^2\) can be obtained from at least one codeword \(c\in C\) by replacing either 1's by 0's in at most \(R\) coordinates or 0's by 1's in at most \(R\) coordinates.
Patric R. J. Östergård +1 more
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On the covering radius of codes
IEEE Transactions on Information Theory, 1985A number of new results for the minimum covering radius of any binary code of a given length and dimension are given. The minimum covering radius for codes of dimension 4 or 5 is determined exactly, and tight bounds are obtained for any dimension when the code length is large.
Ronald L. Graham, Neil J. A. Sloane
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On Lower Bounds For Covering Codes
Designs, Codes and Cryptography, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mahesh C. Bhandari +2 more
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Linear nonbinary covering codes and saturating sets in projective spaces
Advances in Mathematics of Communications, 2011 Let A(R,q) denote a family of covering codes, in which the covering radius R and the size q of the underlying Galois field are fixed, while the code length tends to infinity.
Alexander A Davydov +2 more
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Long packing and covering codes
IEEE Transactions on Information Theory, 1997Let \(C_i\), \(i=1,2,\dots\), denote an infinite family of binary codes with length \(n_i\) tending to infinity, covering radius \(R_i\), and minimum distance \(d_i\). Assume that the limits \(\rho\) and \(\delta\) for the ratios \(R_i/n_i\) and \(d_i/n_i\) exist. The authors study the set \(Y\) (respectively, \(Y_{\text{lin}})\) of possible values \((\
Gérard D. Cohen +3 more
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Linear codes with covering radius 2 and other new covering codes
IEEE Transactions on Information Theory, 1991Infinite families of linear binary codes with covering radius R=2 and minimum distance d=3 and d=4 are given. Using the constructed codes with d=3, R=2, families of covering codes with R>2 are obtained. The parameters of many constructed codes with R >
Ernst M. Gabidulin +2 more
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Sphere coverings and identifying codes
Designs, Codes and Cryptography, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Auger +2 more
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New Constructions of Covering Codes
Designs, Codes and Cryptography, 2001Covering codes and their constructions and a general survey of covering problems are considered in [\textit{G. D. Cohen}, \textit{I. S. Honkala}, \textit{S. N. Litsyn} and \textit{A. C. Lobstein}, Covering Codes. North-Holland Math. Library. Vol. 54. Amsterdam: Elsevier (1997; Zbl 0874.94001)].
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On the covering radius of subcodes of a code
IEEE Transactions on Information Theory, 1991Summary: Let \(C\) be a binary linear code with covering radius \(R\), and \(C_ 0\) a subcode of \(C\) of codimension \(i\). An upper bound is obtained for the covering radius of \(C_ 0\) in terms of \(R\) and \(i\). When \(C_ 0=\{0\}\), the bound becomes the sphere covering bound for \(R\).
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Constructing Covering Codes with Given Automorphisms
Designs, Codes and Cryptography, 1999The authors consider the problem of finding upper bounds on \(K(n,r)\), the minimum number of words in a binary code of length \(n\) and covering radius \(r\). Constructions of covering codes give these bounds on \(K(n,r)\). It is shown how computer searches for covering codes can be speed up by requiring that the code has a given (not necessarily full)
Patric R. J. Östergård +1 more
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