Results 11 to 20 of about 374 (164)
The automorphisms and error orbits of Reed – Solomon codes [PDF]
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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Polar Codes for Automorphism Ensemble Decoding [PDF]
2021 IEEE Information Theory Workshop (ITW), 2021 6 pages, 4 figures, final version of conference paper accepted to IEEE ITW ...
Pillet, C, Bioglio, V, Land, I
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Syndrome spectrums of error orbits in RS-codes [PDF]
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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Quantum codes from algebraic curves with automorphisms [PDF]
Condensed Matter Physics, 2008 Let Χ be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From Χ, under certain conditions, we can construct an algebraic geometry code C.
T.Shaska
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Fault-Tolerant Logical Clifford Gates from Code Automorphisms [PDF]
PRX QuantumWe study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose ...
Hasan Sayginel +4 more
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Automorphisms of Codes in the Grassmann Scheme [PDF]
, 2012 Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are examined on two classical coding problems in the Grassmannian.
Etzion, Tuvi, Vardy, Alexander
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Geometric Goppa codes on Fermat curves [PDF]
Le Matematiche, 2005 We consider a class of codes defined by Goppa’s algebraic-geometric construction on Fermat curves. Automorphisms and decoding of such codes are investigated.
Antonino Giorgio Spera
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On automorphism groups of polar codes [PDF]
CoRROver the past years, Polar codes have arisen as a highly effective class of linear codes, equipped with a decoding algorithm of low computational complexity. This family of codes share a common algebraic formalism with the well-known Reed-Muller codes, which involves monomial evaluations. As useful algebraic codes, more specifically known as decreasing
Jicheng Ma, Guiying Yan
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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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On p-Adic Estimates of Weights in Abelian Codes over Galois Rings [PDF]
, 2005 Let p be a prime. We prove various analogues and generalizations of McEliece's theorem on the p-divisibility of weights of words in cyclic codes over a finite field of characteristic p. Here we consider Abelian codes over various Galois rings.
Katz, Daniel Jerome
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