Results 31 to 40 of about 115,969 (299)
Linking Reversed and Dual Codes of Quasi-Cyclic Codes
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2022 SUMMARY It is known that quasi-cyclic (QC) codes over the finite field F 𝑞 correspond to certain F 𝑞 [ 𝑥 ] -modules. A QC code C is specified by a generator polynomial matrix 𝐺 whose rows generate C as an F 𝑞 [ 𝑥 ] -module.
R. T. Eldin, H. Matsui
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IEEE Transactions on Communications, 2021 In his pioneering work on LDPC codes, Gallager dismissed codes with parity-check matrices of weight two after proving that their minimum Hamming distances grow at most logarithmically with their code lengths.
Xin Xiao +4 more
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Cyclic lowest density MDS array codes [PDF]
, 2009 Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the
Bruck, Jehoshua, Cassuto, Yuval
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New Quasi-Cyclic Codes From Simplex Codes [PDF]
IEEE Transactions on Information Theory, 2007 3 ...
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Algebraic Quasi Cyclic Codes [PDF]
, 2017 في هذا الفصل، تتم مناقشة الرموز المزدوجة والثنائية ثنائية الدوران بناءً على الأعداد الأولية. العديد من الرموز المزدوجة الدوران مزدوجة ذاتيًا. تشكل الرموز الثنائية المزدوجة فئة مهمة من الرموز بسبب قدراتها القوية على تصحيح الأخطاء وبنيتها الرياضية الغنية. تمكن هذه البنية من تحديد توزيع الوزن الكامل للرمز.
Martin Tomlinson +4 more
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Sensors, 2023 The traditional LDPC encoding and decoding system is characterized by low throughput and high resource consumption, making it unsuitable for use in cost-efficient, energy-saving sensor networks.
Yuxuan Sun +5 more
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IEEE Access, 2019 Recently, rate-compatible raptor-like quasi-cyclic low-density parity-check (RL-QC-LDPC) codes, which are a typical class of multi-edge type LDPC codes with excellent performance and high flexibility, have been adopted in the technical specification of ...
Yushu Zhang +3 more
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Applied Mathematics Letters, 2002 AbstractOne of the most important problems of coding theory is to construct codes with best possible minimum distances. In this paper, we use the algebraic structure of quasi-cyclic codes and the BCH type bound on the minimum distance to search for quasicyclic codes over F5, the finite field with five elements, which improve the minimum distances of ...
Siap, I, Aydin, N
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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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