Results 11 to 20 of about 19,178 (185)
Twisted Reed-Solomon Codes [PDF]
2017 IEEE International Symposium on Information Theory (ISIT), 2017 We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are
Beelen, Peter +2 more
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Repairing Reed-Solomon Codes [PDF]
Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, 2016 We study the performance of Reed-Solomon (RS) codes for the \em exact repair problem \em in distributed storage. Our main result is that, in some parameter regimes, Reed-Solomon codes are optimal regenerating codes, among MDS codes with linear repair ...
Guruswami, Venkatesan, Wootters, Mary
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The automorphisms and error orbits of Reed – Solomon codes
Доклады Белорусского государственного университета информатики и радиоэлектроники, 2020 The purpose of this work with its results presented in the article was to develop and transfer to the class of Reed – Solomon codes (RS-codes) the basic provisions of the theory of syndrome norms (TNS), previously developed for the noise-resistant coding
S. I. Semyonov, V. A. Lipnitsky
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Balanced Reed-Solomon codes [PDF]
2016 IEEE International Symposium on Information Theory (ISIT), 2016 We consider the problem of constructing linear Maximum Distance Separable (MDS) error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of non-zero entries, and balanced means that every column contains the same number of non-zero entries.
Halbawi, Wael +2 more
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Decoding Reed–Solomon Skew-Differential Codes [PDF]
IEEE Transactions on Information Theory, 2021 A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making them fully accesible for everyone.
Jose Gomez-Torrecillas +2 more
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Quantum Reed—Solomon Codes [PDF]
, 1999 After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed.
Grassl, Markus +2 more
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Lifted projective Reed–Solomon codes [PDF]
Designs, Codes and Cryptography, 2018 Lifted Reed-Solomon codes, introduced by Guo, Kopparty and Sudan in 2013, are known as one of the few families of high-rate locally correctable codes. They are built through the evaluation over the affine space of multivariate polynomials whose restriction along any affine line can be interpolated as a low degree univariate polynomial. In this work, we
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Weighted Reed–Solomon convolutional codes
Linear and Multilinear Algebra, 2023 In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to the context of convolutional codes.
Alfarano, Gianira N. +3 more
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Reed-Solomon Coded Cooperative Spatial Modulation Based on Nested Construction for Wireless Communication [PDF]
Radioengineering, 2021 This paper proposes the Reed-Solomon coded cooperative spatial modulation (RSCC-SM) scheme based on nested construction of two Reed-Solomon (RS) codes over quasi-static Rayleigh fading channel.
C. L. Zhao, F. F. Yang, D. K. Waweru
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Lifted Multiplicity Codes and the Disjoint Repair Group Property [PDF]
, 2019 Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code.
Li, Ray, Wootters, Mary
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