Results 1 to 10 of about 5,176 (95)
Skew Constacyclic Codes over a Non-Chain Ring [PDF]
Entropy, 2023 In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+1⟩ and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a
Mehmet Emin Köroğlu, Mustafa Sarı
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Low-Complexity Automorphism Ensemble Decoding of Reed-Muller Codes Using Path Pruning [PDF]
EntropyThe newly developed automorphism ensemble decoder (AED) leverages the rich automorphisms of Reed–Muller (RM) codes to achieve near maximum likelihood (ML) performance at short code lengths.
Kairui Tian, Rongke Liu, Zheng Lu
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On the Dimensions of Hermitian Subfield Subcodes from Higher-Degree Places [PDF]
EntropyThe focus of our research is the examination of Hermitian curves over finite fields, specifically concentrating on places of degree three and their role in constructing Hermitian codes.
Sabira El Khalfaoui, Gábor P. Nagy
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Quasi-Optimal Path Convergence-Aided Automorphism Ensemble Decoding of Reed–Muller Codes [PDF]
EntropyBy exploiting the rich automorphisms of Reed–Muller (RM) codes, the recently developed automorphism ensemble (AE) successive cancellation (SC) decoder achieves a near-maximum-likelihood (ML) performance for short block lengths.
Kairui Tian +3 more
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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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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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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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An MDS-PIR Capacity-Achieving Protocol for Distributed Storage Using Non-MDS Linear Codes [PDF]
, 2018 We propose a private information retrieval (PIR) protocol for distributed storage systems with noncolluding nodes where data is stored using an arbitrary linear code.
Amat, Alexandre Graell i +3 more
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Generic BCH codes. Polynomial-norm error decoding
Журнал Белорусского государственного университета: Математика, информатика, 2020 The classic Bose – Chaudhuri – Hocquenghem (BCH) codes is famous and well-studied part in the theory of error-correcting codes. Generalization of BCH codes allows us to expand the range of activities in the practical correction of errors.
Alexander V. Kushnerov +1 more
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Properties of triple error orbits G and their invariants in Bose – Chaudhuri – Hocquenghem codes C7
Весці Нацыянальнай акадэміі навук Беларусі: Серыя фізіка-тэхнічных навук, 2019 This work is the further development of the theory of norms of syndromes: the theory of polynomial invariants of G-orbits of errors expands with the group G of automorphisms of binary cyclic BCH codes obtained by joining the degrees of cyclotomic ...
V. A. Lipnitski, A. U. Serada
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