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Lower Bounds for qary Codes with Large Covering Radius
"... Let Kq(n,R) denote the minimal cardinality of a qary code of length n and covering radius R. Recently the authors gave a new proof of a classical lower bound of Rodemich on Kq(n,n−2) by the use of partition matrices and their transversals. In this paper we show that, in contrast to Rodemich’s origi ..."
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Let Kq(n,R) denote the minimal cardinality of a qary code of length n and covering radius R. Recently the authors gave a new proof of a classical lower bound of Rodemich on Kq(n,n−2) by the use of partition matrices and their transversals. In this paper we show that, in contrast to Rodemich’s
New Constructions for qary Covering Codes
"... Upper bounds on Kq (n; R), the minimum number of codewords in a qary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance ..."
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Upper bounds on Kq (n; R), the minimum number of codewords in a qary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum
Identifying Codes in qary Hypercubes
"... Let q be any integer ≥ 2. In this paper, we consider the qary ndimensional cube whose vertex set is Z n q and two vertices (x1,..., xn) and (y1,..., yn) are adjacent if their Lee distance is 1. As a natural extension of identifying codes in binary Hamming spaces, we further study identifying codes ..."
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Let q be any integer ≥ 2. In this paper, we consider the qary ndimensional cube whose vertex set is Z n q and two vertices (x1,..., xn) and (y1,..., yn) are adjacent if their Lee distance is 1. As a natural extension of identifying codes in binary Hamming spaces, we further study identifying
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 741 (23 self)
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We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
Understanding Code Mobility
 IEEE COMPUTER SCIENCE PRESS
, 1998
"... The technologies, architectures, and methodologies traditionally used to develop distributed applications exhibit a variety of limitations and drawbacks when applied to large scale distributed settings (e.g., the Internet). In particular, they fail in providing the desired degree of configurability, ..."
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Cited by 549 (34 self)
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, scalability, and customizability. To address these issues, researchers are investigating a variety of innovative approaches. The most promising and intriguing ones are those based on the ability of moving code across the nodes of a network, exploiting the notion of mobile code. As an emerging research field
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
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Cited by 557 (9 self)
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An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Results 1  10
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1,467,287