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On deep holes of generalized Reed-Solomon codes
AIMS Mathematics, 2016 Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q-1, k]q if its Lagrange interpolation polynomial is the sum of ...
Shaofang Hong, Rongjun Wu
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Low-Complexity Chase Decoding of Reed–Solomon Codes Using Channel Evaluation [PDF]
Entropy, 2022 A novel time-varying channel adaptive low-complexity chase (LCC) algorithm with low redundancy is proposed, where only the necessary number of test vectors (TVs) are generated and key equations are calculated according to the channel evaluation to reduce
Hao Wang +4 more
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Entanglement-Assisted Quantum Codes from Cyclic Codes [PDF]
Entropy, 2022 Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer ...
Francisco Revson F. Pereira +1 more
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Some new QEC MDS codes with large minimum distance [PDF]
Scientific ReportsThe advancement of Quantum Error-Correcting (QEC) Maximum Distance Separable (MDS) codes holds substantial importance in practical applications, substantially augmenting the reliability and efficiency of quantum communication and computing.
Lanqiang Li +3 more
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Symbol-level iterative information set decoding of RS codes
Alexandria Engineering Journal, 2023 This paper presents the implementation of a low-complex iterative symbol-level decoding scheme for Reed-Solomon codes. Most soft-decision iterative decoders for Reed-Solomon codes work on a bit level due to the efficient passing of soft information due ...
Yuval Genga +2 more
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A Topological View of Reed–Solomon Codes
Mathematics, 2021 We studied a particular class of well known error-correcting codes known as Reed–Solomon codes. We constructed RS codes as algebraic-geometric codes from the normal rational curve.
Alberto Besana, Cristina Martínez
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Mathematics, 2020 We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-dimensional Schur
Austin Allen +6 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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IEEE Access, 2023 The revolution in the field of information processing systems has created a huge demand for reliable and enhanced data storage capabilities. This demand is being met by advances in channel coding algorithms along with upward scaling of the capacities of ...
G. Achala +2 more
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Decoding algorithms for Goppa codes with errors and erasures [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2022 In 1978, McEliece built the first public key cryptosystem based on error-correcting codes. This cryptosystem based on Goppa codes is considered promising and cryptographically stable, taking into account quantum computing.
Ratseev, Sergey Mihailovich +1 more
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