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Error correction by Reed–Solomon codes using its automorphisms
Весці Нацыянальнай акадэміі навук Беларусі: Серыя фізіка-тэхнічных навук, 2021 The article explores the syndrome invariants of АГ-group of automorphisms of Reed–Solomon codes (RS-codes) that are a joint group of affine and cyclic permutations. The found real invariants are a set of norms of N Г-orbits that make up one or another АГ-
V. A. Lipnitsky, S. I. Semyonov
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Optimization and FPGA implementation of RS coding algorithm
Dianzi Jishu Yingyong, 2020 Aiming at the problems of large amount of computation and high complexity of multiplication of Galois Field(GF) in the common RS coding algorithm, the RS coding module is optimized and the multiplier factor is obtained.
Li Jinming, Liu Mengxin, Cheng Naipeng
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Low power design and ASIC research of RS code
Journal of Measurement Science and Instrumentation, 2023 In order to solve the low-power design of reed-solomon (RS) code, it is carried out from different design levels such as system architecture, RTL level and gate level, etc. And it is practiced in application specific integrated circuit (ASIC) design. The
ZHANG Pingping, LI Jinming
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Soil Security, 2022 Grazing intensity in integrated crop-livestock systems (ICLS) can affect soil aggregation and C stabilization and, consequently, the soil condition and agricultural sustainability.
Bruna Possobon Soares +9 more
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Food Technology and Biotechnology, 2022 Research background. Cheese whey and whey permeate are dairy industry by-products usually sent to effluent treatment or incorrectly disposed in the environment, generating costs for the production of dairy products and environmental problems due to the ...
Marcos Aurélio Dahlem Júnior +7 more
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Water Science and Technology, 2023 Pharmaceutical compounds can reach water bodies through sewage systems. The process of water treatment is insufficient for the removal of these contaminants.
Letícia Reggiane de Carvalho Costa +1 more
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Peterson-Gorenstein-Zierler algorithm for skew RS codes [PDF]
CoRR, 2017 We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure.
José Gómez-Torrecillas +2 more
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Syndrome spectrums of error orbits in RS-codes
Системный анализ и прикладная информатика, 2020 This article is devoted to the research of the properties of syndromes of errors in Reed-Solomon codes. RS-codes are built on non-binary alphabets. So, unlike BCH-codes, RS-codes contain an extremely large variety of correctable errors.
V. A. Lipnitski, S. I. Semyonov
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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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Soft-decision decoding of RS codes [PDF]
Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., 2005 By introducing a few simplifying assumptions we derive a simple condition for successful decoding using the Koetter-Vardy algorithm for soft-decision decoding of RS codes. We show that the algorithm has a significant advantage over hard decision decoding when the code rate is low, when two or more sets of received symbols have substantially different ...
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