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Mathematics, 2023 Let k,m be positive integers and F2m be a finite field of order 2m of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring Sk=F2m[v1,v2,…,vk]⟨vi2−αivi,vivj−vjvi⟩, for i,j=1,2,3,…,k, where αi
Shakir Ali +3 more
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On quantum tensor product codes [PDF]
Quantum Information and Computation, 2017 We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs ...
Jihao Fan +3 more
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A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product Codes [PDF]
International Conference on Quantum Computing and Engineering, 2020 We provide a numerical investigation of two families of subsystem quantum codes that are related to hypergraph product codes by gauge-fixing. The first family consists of the Bravyi-Bacon-Shor (BBS) codes which have optimal code parameters for subsystem ...
Muyuan Li, Theodore J. Yoder
semanticscholar +1 more source
Refined Reliability Combining for Binary Message Passing Decoding of Product Codes [PDF]
Journal of Lightwave Technology, 2020 We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance decoding (iBDD)
Alireza Sheikh +3 more
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Bias-tailored quantum LDPC codes [PDF]
Quantum, 2023 Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise.
Joschka Roffe +4 more
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On tensor products of CSS codes [PDF]
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, 2019 CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product \otimes which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given
Audoux, Benjamin, Couvreur, Alain
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Balanced Product Quantum Codes [PDF]
IEEE Transactions on Information Theory, 2021 23 pages, 11 ...
Nikolas P. Breuckmann +1 more
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Single parity check product codes [PDF]
, 2022 Questo elaborato presenta ed analizza nel dettaglio i Single Parity Check Product Codes; vengono inizialmente esaminati i concetti alla base di product codes generici, per poi passare ad una focalizzazione sui Single Parity Check Product Codes e sulla ...
Savorgnan, Ilaria
core
Minimal State-Space Representation of Convolutional Product Codes
Mathematics, 2021 In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes.
Joan-Josep Climent +3 more
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An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes [PDF]
MATEC Web of Conferences, 2021 In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes.
Yao Yu, Ma Yuena, Li Husheng, Lv Jingjie
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