Results 11 to 20 of about 5,913 (208)
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
Lavauzelle, Julien, Julien Lavauzelle
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CoRR, 2018 We introduce Reed-Solomon-Gabidulin codes which is, at the same time, an extension to Reed-Solomon codes on the one hand and Gabidulin codes on the other hand. We prove that our codes have good properties with respect to the minimal distance and design an efficient decoding algorithm.
Xavier Caruso, Amaury Durand
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Duals of linearized Reed–Solomon codes
Designs, Codes and Cryptography, 2022 We give a description of the duals of linearized Reed-Solomon codes in terms of codes obtained by taking residues of Ore rational functions. Our construction shows in particular that, under some assumptions on the base field, the class of linearized Reed-Solomon codes is stable under duality.
Caruso, Xavier, Durand, Amaury
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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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The automorphism groups of Reed-Solomon codes
Journal of Combinatorial Theory, Series A, 1987 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dür, Arne
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Reliability on QR codes and Reed-Solomon codes
CoRRThis study addresses the use of Reed-Solomon error correction codes in QR codes to enhance resilience against failures. To fully grasp this approach, a basic cryptographic context is provided, necessary for understanding Reed-Solomon codes. The study begins by defining a code and explores key outcomes for codes with additional properties, such as ...
Bajaj, Bhavuk Sikka
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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.
Markus Grassl +2 more
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FNT-based reed-solomon erasure codes [PDF]
, 2009 This paper presents a new construction of Maximum-Distance Separable (MDS) Reed-Solomon erasure codes based on Fermat Number Transform (FNT). Thanks to FNT, these codes support practical coding and decoding algorithms with complexity O(n log n), where n ...
Soro, Alexandre +3 more
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Improved adaptive belief propagation algorithm with reduced complexity for concatenated SPC‐RS codes
Electronics Letters, 2023 In this letter, a novel single parity check‐aided minimum sum (SPC‐aided MS) algorithm is proposed. A cascaded compiled code scheme is used to approximate the adaptive belief propagation (ABP) algorithm for Reed–Solomon (RS) codes using the min sum (MS ...
Yuan Cheng +5 more
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Reed-Solomon Codes (Codici di Reed-Solomon) [PDF]
, 2022 This work offers a general overview on Reed-Solomon codes as a subclass of cyclic codes and BCH codes, using a mathematical approach to describe their practical aspects.
Martini, Tommaso
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