Results 21 to 30 of about 1,960 (155)
Decomposing Quasi-Cyclic Codes
Electronic Notes in Discrete Mathematics, 2001 Abstract A new algebraic approach to quasi-cyclic codes is introduced. Technical tools include the Chinese Remainder Theorem, the Discrete Fourier Transform, Chain rings. The main results are a characterization of self-dual quasi-cyclic codes, a trace representation that generalizes that of cyclic codes, and an interpretation of the squaring and ...
Ling, S., Solé, P.
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Quantum Quasi-Cyclic LDPC Codes [PDF]
2007 IEEE International Symposium on Information Theory, 2007 In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our proposed codes have lots of variations for length, code rate. These codes are obtained by a descrete mathematical
Hagiwara, Manabu, Imai, Hideki
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Finite Fields and Their Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tong, Hongxi, Ding, Yang
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4-CYCLE FREE APM LDPC CODES WITH AN EXPLICIT CONSTRUCTION [PDF]
Journal of Algebraic Systems, 2021 Recently, a class of low-density parity-check codes based on affine permutation matrices, called APM-LDPC codes, have been considered which have some advantages than quasi-cyclic (QC) LDPC codes in terms of minimum-distance, cycle distribution, and error-
Z. Gholami, M. Gholami
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New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes
IEEE Access, 2019 In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner ...
Jingjie Lv, Ruihu Li, Junli Wang
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The design of structured LDPC codes with algorithmic graph construction [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2022 Low-Density Parity-Check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme.
Wojciech Sułek
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High-Speed Reconciliation for CVQKD Based on Spatially Coupled LDPC Codes
IEEE Photonics Journal, 2018 The speed of continuous variable quantum key distribution is limited by the reconciliation efficiency and the reconciliation frame error rate (FER) in the reconciliation phase.
Xue-Qin Jiang +3 more
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Quasi-cyclic constructions of quantum codes
Finite Fields and Their Applications, 2018 We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum distance of the involved codes.
Carlos Galindo +2 more
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Efficient Encryption From Random Quasi-Cyclic Codes [PDF]
IEEE Transactions on Information Theory, 2018 We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based on the difficulty of decoding random linear codes from random errors of low weight.
Carlos Aguilar-Melchor +4 more
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Combinatorial design-based quasi-cyclic LDPC codes with girth eight
Digital Communications and Networks, 2018 This paper presents a novel regular Quasi-Cyclic (QC) Low Density Parity Check (LDPC) codes with column-weight three and girth at least eight. These are designed on the basis of combinatorial design in which subsets applied for the construction of ...
Sina Vafi, Narges Rezvani Majid
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