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Combinatorica, 2007
What is the maximum possible number, f3(n), of vectors of length n over {0,1,2} such that the Hamming distance between every two is even? What is the maximum possible number, g3(n), of vectors in {0,1,2}n such that the Hamming distance between every two is odd?
Noga Alon, Eyal Lubetzky
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What is the maximum possible number, f3(n), of vectors of length n over {0,1,2} such that the Hamming distance between every two is even? What is the maximum possible number, g3(n), of vectors in {0,1,2}n such that the Hamming distance between every two is odd?
Noga Alon, Eyal Lubetzky
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Straggler-Proofing Massive-Scale Distributed Matrix Multiplication with D-Dimensional Product Codes
International Symposium on Information Theory, 2018Distributed computing allows for large-scale computation and machine learning tasks by enabling parallel computing at massive scale. A critical challenge to speeding up distributed computing comes from stragglers, a crippling bottleneck to system ...
Tavor Z. Baharav +3 more
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Chaos for Speech Coding and Production
2011The presence of nonlinearity and chaotic behavior in the human speech production system has been reported previously; however to date chaotic dynamics has not been widely exploited in speech coding and artificial speech production algorithms. In this paper we illustrate how we can utilize chaotic dynamics in speech coding and synthesis and discuss how ...
Behnam Kia +2 more
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Quantum Information Processing, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Asymptotic performance of product codes
1999 IEEE International Conference on Communications (Cat. No. 99CH36311), 2003This paper presents the asymptotic performance of Hamming and extended Hamming product codes for the binary symmetric channel and the additive white Gaussian noise (AWGN) channel. Simulation results for very low complexity high dimensional single parity check product codes on the AWGN channel are also given.
David M. Rankin, T. Aaron Gulliver
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Journal of Algebra and its Applications, 2023
A. Duarte, A. Pereira, C. Polcino Milies
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A. Duarte, A. Pereira, C. Polcino Milies
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Trellis Properties of Product Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2005In this paper, we study trellis properties of the tensor product (product code) of two linear codes, and prove that the tensor product of the lexicographically first bases for two linear codes in minimal span form is exactly the lexicographically first basis for their product code in minimal span form, also the tensor products of characteristic ...
Kan, H., Shen, H.
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Product codes and the singleton bound
1994Minimum distance is not always the most determinant factor to acheive high performance for error correction. Of course the knowledge of the whole weight distribution of the code is more accurate than the knowledge of the mere minimum distance, and the phenomenon amplifies for a high noise level.
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Further results on product codes
IEEE Transactions on Information Theory, 1970A new class of codes, called product generator codes, which are similar to Elias's iterated codes, are investigated. An important subclass of these codes is the generalized Reed-Muller codes. If the original codes that are iterated to produce a product code are L_1 and L_2 -step orthogonalizable, then the product code is ( L_1 + L_2 - 1 )-step ...
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