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Propelinear structure of Z2klinear codes
, 907
"... Let C be an additive subgroup of Z n 2k for any k ≥ 1. We define a Gray map Φ: Z n 2k − → Z kn 2 such that Φ(C) is a binary propelinear code and, hence, a Hammingcompatible group code. Moreover, Φ is the unique Gray map such that Φ(C) is Hammingcompatible group code. Using this Gray map we discuss ..."
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Let C be an additive subgroup of Z n 2k for any k ≥ 1. We define a Gray map Φ: Z n 2k − → Z kn 2 such that Φ(C) is a binary propelinear code and, hence, a Hammingcompatible group code. Moreover, Φ is the unique Gray map such that Φ(C) is Hammingcompatible group code. Using this Gray map we
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
 Journal of the ACM
, 1998
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes ..."
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Cited by 390 (2 self)
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to Christofides) achieves a 3/2approximation in polynomial time. We also give similar approximation schemes for some other NPhard Euclidean problems: Minimum Steiner Tree, kTSP, and kMST. (The running times of the algorithm for kTSP and kMST involve an additional multiplicative factor k.) The previous best
Understanding FaultTolerant Distributed Systems
 COMMUNICATIONS OF THE ACM
, 1993
"... We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design ..."
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Cited by 374 (23 self)
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alternatives, we discuss their relative merits and we give examples of systems which adopt one approach or the other. The aim is to introduce some order in the complex discipline of designing and understanding faulttolerant distributed systems.
On the Minimum Distance of Generalized LDPC Codes
"... Abstract — We study necessary conditions which have to be satisfied in order to have LDPC codes with linear minimum distance. We give two conditions of this kind in this paper. These conditions are not met for several interesting code families: this shows that they are not asymptotically good. The s ..."
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Cited by 1 (1 self)
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and if there are such cycles in the protograph, the second condition seems to capture really well the linear minimum distance character of the code. This is illustrated by a code family which is asymptotically good for which there is a cycle linking all the variable nodes of degree 2 together. Surprisingly, this family
Minimum Distance Bounds for Expander Codes
"... Abstract — Several expander code constructions and their parameters are surveyed. New generalized expander codes are introduced and their properties are compared with the properties of the existing constructions. Finally, some possible directions to extend the current research on expander codes are ..."
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Abstract — Several expander code constructions and their parameters are surveyed. New generalized expander codes are introduced and their properties are compared with the properties of the existing constructions. Finally, some possible directions to extend the current research on expander codes
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
Fingerprinting with Minimum Distance Decoding
, 710
"... This work adopts an information theoretic framework for the design of collusionresistant coding/decoding schemes for digital fingerprinting. More specifically, the minimum distance decision rule is used to identify 1 out of t pirates. Achievable rates, under this detection rule, are characterized i ..."
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Cited by 1 (0 self)
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rates, with minimum distance decoding, under any collusion attack that satisfies the marking assumption. For t = 2 pirates, we show that the rate 1 − H(0.25) ≈ 0.188 is achievable using an ensemble of random linear codes. For t ≥ 3, the existence of a nonresolvable collusion attack, with minimum
Quantum codes of minimum distance two
 IEEE Trans. Inf. Theory
, 1999
"... Abstract. It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With this in mind, we present a number of results on codes ..."
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Cited by 11 (0 self)
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on codes of minimum distance 2. We first compute the linear programming bound on the dimension of such a code, then show that this bound can only be attained when the code either is of even length, or is of length 3 or 5. We next consider questions of uniqueness, showing that the optimal code of length 2
Spectra and minimum distances of Repeat Multiple Accumulate codes
"... Abstract — In this paper we consider ensembles of codes, denoted RA m, obtained by a serial concatenation of a repetition code and m accumulate codes through uniform random interleavers. We analyze their average spectrum functions for each m showing that they are equal to 0 below a threshold distanc ..."
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Cited by 4 (1 self)
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distance ǫm and positive beyond it. One of our main results is to prove that these average spectrum functions form a notincreasing sequence in m converging uniformly to a limit spectrum function which is equal to the maximum between the average spectrum function of the classical linear random ensemble
Generalized minimum distance iterative decoding of Tanner codes
 IEEE Comm. Letters
"... Abstract — In this Letter, we present a lineartime decoding algorithm for Tanner codes that can correct errors up to close to half the minimum distance of the code. The algorithm is a simple generalization to the iterative decoding algorithm of expander codes proposed by Skachek and Roth [3]. Index ..."
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Cited by 1 (0 self)
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Abstract — In this Letter, we present a lineartime decoding algorithm for Tanner codes that can correct errors up to close to half the minimum distance of the code. The algorithm is a simple generalization to the iterative decoding algorithm of expander codes proposed by Skachek and Roth [3
Results 1  10
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