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IEEE Globecom Workshops (Gc Workshops 2009)

作者： Marazin, M. Gautier, R. Burel, G. Univ Europeenne Bretagne Rennes France

ISBN: (纸本)9781424456246

Digital communication systems are in perpetual evolution in order to respond to the new user expectations and to new applications transmissions constraints, in term of data rate or reliability. With this fast development of new communication standards, it becomes very difficult for users and also for communications devices producers, to stay compatible with all standards used and with the oncoming ones. For that reason, cognitive radio systems seem to provide an interesting solution to this problem. The conception of intelligent receiver able to adapt itself to a specific transmission context and to blindly estimate the transmitter parameters is a promising solution for the future. In such context, new coding schemes like turbocodes, Low-Density Parity-Check (LDPC) or concatenated codes are developed to increase transmission robustness without significant degradation of the data rate. It is why we have developed a method, described in this paper, dedicated to the blind identification of convolutional encoders usually used in many standards. Moreover, an analysis of the method performances is detailed.

关键词： Cognitive radio intelligent receiver blind identification convolutional encoder dual code

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The dual code of any (δ plus αu²)-constacyclic code over F2m[u]/⟨u⁴⟩ of oddly even length

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DISCRETE MATHEMATICS 2019年第8期342卷 2179-2191页

作者： Gao, Yun Fu, Fang-Wei Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China

Let F-2m be a finite field of cardinality 2(m), R = F-2m[u]/ = F-2m + uF(2m) +u(2)F(2m) + u(3)F(2m) (u(4) = 0) which is a finite chain ring, and n is an odd positive integer. For any delta, alpha is an element of F-2m... 详细信息

Let F-2m be a finite field of cardinality 2(m), R = F-2m[u]/< u(4)> = F-2m + uF(2m) +u(2)F(2m) + u(3)F(2m) (u(4) = 0) which is a finite chain ring, and n is an odd positive integer. For any delta, alpha is an element of F-2m(x) an explicit representation for the dual code of any (delta + alpha u(2))-constacyclic code over R of length 2n is given. And some dual codes of (1 + u(2))-constacyclic codes over R of length 14 are constructed. For the case of delta = 1, all distinct self-dual (1 + alpha u(2))-constacyclic codes over R of length 2n are determined. (C) 2019 Elsevier B.V. All rights reserved.

关键词： dual code Self-dual code Constacyclic code

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dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric laminar flows

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AEROSPACE SCIENCE AND TECHNOLOGY 2008年第2期12卷 135-149页

作者： Hejranfar, Kazem Moghadam, Rarnin Kamali Esfahanian, Vahid Sharif Univ Technol Dept Aerosp Engn Tehran 113658639 Iran Univ Tehran Dept Mech Engn Tehran 113654563 Iran

An appropriate combination of the thin-layer Navier-Stokes (TLNS) and parabolized Navier-Stokes (PNS) solvers is used to accurately and efficiently compute hypersonic flowfields of equilibrium air around blunt-body configurations. The TLNS equations are solved in the nose region to provide the initial data plane needed for the solution of the PNS equations. Then the PNS equations are employed to efficiently compute the flowfield for the afterbody region by using a space marching procedure. Both the TLNS and PNS equations are numerically solved by using the efficient implicit non-iterative finite-difference algorithm of Beam and Warming. A shock fitting technique is used in both the TLNS and PNS codes to obtain accurate solution in the vicinity of the shock. In the regions of the flowfield with upstream influences, the globally iterated PNS (IPNS) equations, which are computationally more efficient than the TLNS equations, can be used to improve the accuracy of the results. To validate the results of the developed TLNS code and study real gas effects on the flowfield, hypersonic laminar flow over a sphere at Mach number of 11.26 is computed. The computations are performed for hypersonic laminar flow over 5 degrees long slender blunt cone at Mach number of 19.25 to demonstrate the accuracy and efficiency of using the present TLNS-PNS methodology. To show the capability and robustness of the present solution procedure, the comparisons are also made with the wall heat-transfer data on a 12.84 degrees/7 degrees bicone at Mach number of 6.89 and freestream temperature of 1604 K. The results of these computations are found to be in good agreement with available numerical and experimental data. The results of the perfect gas for these cases are also presented and the effects of real gas on the flowfield characteristics are studied in both the TLNS and PNS solutions. (c) 2007 Elsevier Masson SAS. All rights reserved.

关键词： dual code equilibrium hypersonic flows blunt-body configurations shock fitting technique

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Improved Lower Bounds on the Minimum Distances of the dual codes of Primitive Narrow-Sense BCH codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第1期71卷 330-347页

作者： Gan, Chunyu Li, Chengju Mesnager, Sihem Xie, Conghui Zhou, Haiyan East China Normal Univ MoE Engn Res Ctr Software Hardware Codesign Techno Shanghai 200062 Peoples R China Univ Paris VIII Dept Math F-93526 St Denis France Univ Sorbonne Paris Cite Lab Anal Geometry & Applicat LAGA UMR 7539 CNRS F-93430 Villetaneuse France Polytech Inst Paris Telecom Paris F-91120 Palaiseau France Jinan Univ Coll Informat Sci & Technol Cyber Secur Guangzhou 510632 Guangdong Peoples R China Nanjing Normal Univ Sch Math Sci Nanjing 210023 Peoples R China Nanjing Normal Univ Inst Math Nanjing 210023 Peoples R China

In coding theory, the well-known class of block codes, Bose-Chaudhuri-Hocquenghem codes (BCH codes), form a class of cyclic error-correcting codes constructed using polynomials over a finite field. They are used for various critical practical applications in communication and storage due to their efficient encoding and decoding algorithms. In the past sixty years, significant progress has been made in understanding BCH codes' dimensions and minimum distances. However, there has been limited research on the minimum distances of the dual codes of BCH codes, making it challenging to determine their actual minimum distances. Therefore, developing accurate lower bounds on the minimum distances of the dual codes of BCH codes is crucial and exciting. In this paper, we primarily use the multiplier technique proposed by Huffman and Pless to investigate the lower bounds on minimum distances of the dual codes C-(q,q(m)-1,delta)(perpendicular to) of the primitive narrow-sense BCH codes with designed distance delta . When q = p(e) with e >= 2 , we improve the lower bounds on minimum distances of the dual codes C-(q,q(m)-1,delta)(perpendicular to) in the ranges p(ei)-p(e-1)+2 <=delta <= p(ei+e-1)-p(e-1)+1 , where m >= 2 and 1 <= i <= m-1 . These new lower bounds are much tighter than the previously known bounds in the literature. This technique also applies to the study of binary dual codes C-(2,2(m)-1,delta)(perpendicular to) , for which we obtain tight lower bounds for delta = 2(t) , where m >= 5 is odd and 2 <= t <= m-3 is even.

关键词： codes Linear codes Polynomials Galois fields Generators Error correction codes Encoding Decoding codecs Vectors Linear code cyclic code BCH code dual code multiplier

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Characterizing a Generator Polynomial Matrix for the dual of a Multi-Twisted code

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MATHEMATICAL NOTES 2024年第3-4期116卷 777-792页

作者： Taki Eldin, R. F. Ain Shams Univ Fac Engn Cairo 11517 Egypt Egypt Univ Informat Cairo 15702 Egypt

The class of multi-twisted (MT) codes generalizes the classes of cyclic, constacyclic, quasi-cyclic, quasi-twisted, and generalized quasi-cyclic codes. We establish the correspondence between MT codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document} of index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q[x]$$\end{document}-submodules of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(\mathbb{F}_q[x]\right)<^>\ell$$\end{document}. Thus, a basis of an MT code exists and is used to build a generator polynomial matrix (GPM). We prove some GPM properties, for example, relationship to code dimension, the identical equation, Hermite normal form. Hence, we prove a GPM formula for the dual code of an MT code. Finally, we obtain the necessary and sufficient conditions for the self-orthogonality and self-duality of MT codes.

关键词： multi-twisted code Generator polynomial matrix dual code Hermite normal form

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Repeated-root constacyclic codes of length kslmpn over finite fields

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FINITE FIELDS AND THEIR APPLICATIONS 2025年 101卷

作者： Zhang, Qi Wang, Weiqiong Luo, Shuyu Li, Yue Changan Univ Sch Sci Xian 710064 Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China

For different odd primes k , l , p , and positive integers s , m , n , the polynomial x k s l m p n - lambda in F q [x] is explicitly factorized, where p is the characteristic of F q , lambda is an element of F q & lowast;. All repeated-root constacyclic codes and their dual codes of length k s l m p n over F q are characterized. In addition, the characterization and enumeration of all linear complementary dual (LCD) cyclic and negacyclic codes of length k s l m p n over F q are obtained. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Finite field Constacyclic code Generator polynomial dual code LCD code

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Construction of High-Rate Convolutional codes Using dual codes*

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2023年第3期E106A卷 375-381页

作者： Moriya, Sen Sasano, Hiroshi Kindai Univ Fac Sci & Engn Higashiosaka 5778502 Japan Kindai Univ Cyber Informat Res Inst Higashiosaka 5778502 Japan

In this study, we consider techniques for searching high -rate convolutional code (CC) encoders using dual code encoders. A low-rate (R = 1/n) CC is a dual code to a high-rate (R = (n - 1)/n) CC. According to our past studies, if a CC encoder has a high performance, a dual code encoder to the CC also tends to have a good performance. However, it is not guaranteed to have the highest performance. We consider a method to obtain a high-rate CC encoder with a high performance using good dual code encoders, namely, high-performance low-rate CC encoders. We also present some CC encoders obtained by searches using our method.

关键词： convolutional code dual code weight spectrum

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Quasi-cyclic complementary dual codes

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FINITE FIELDS AND THEIR APPLICATIONS 2016年第0期42卷 67-80页

作者： Guneri, Cem Ozkaya, Buket Sole, Patrick Sabanci Univ FENS TR-34956 Istanbul Turkey Univ Paris Saclay CNRS LTCI F-75013 Paris France King Abdulaziz Univ Dept Math Jeddah Saudi Arabia

Linear complementary dual codes are linear codes that intersect with their dual trivially. Quasi-cyclic codes that are complementary dual are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian linear complementary dual codes are introduced to that end and their cyclic subclass is characterized. Constructions of quasi-cyclic complementary dual codes from codes over larger alphabets are given. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Quasi-cyclic code LCD code dual code

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Construction of High-Rate Punctured Convolutional codes through dual codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2015年第7期E98A卷 1579-1583页

作者： Moriya, Sen Kikuchi, Kana Sasano, Hiroshi Kinki Univ Sch Sci & Engn Higashiosaka Osaka 5778502 Japan

This paper considers a method for constructing good highrate punctured convolutional codes through dual codes. A low-rate R = 1/n convolutional code has a dual code identical to a punctured convolutional code with rate R = (n - 1)/n. This implies that a low-rate R = 1/n convolutional code encoder can help the search of punctured convolutional code encoders. This paper provides the procedures that obtain all the useful dual code encoders to a given CC with rate R = 1/n easily, and the best PCC encoder with rate R = (n - 1)/n among the encoders we derive from all the obtained dual code encoders. This paper also shows an example of the PCC the procedures obtain from some CC.

关键词： convolutional code punctured code dual code weight spectrum

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Efficient Search for High-Rate Punctured Convolutional codes Using dual codes

Efficient Search for High-Rate Punctured Convolutional Codes...

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38th Symposium on Information Theory and its Applications (SITA)

作者： Moriya, Sen Kikuchi, Kana Sasano, Hiroshi Kindai Univ Sch Sci & Engn Higashiosaka Osaka 5778502 Japan

In this study, we consider techniques to search for highrate punctured convolutional code (PCC) encoders using dual code encoders. A low-rate R = 1/n convolutional code (CC) has a dual code that is identical to a PCC with rate R = (n - 1)/n. This implies that a rate R = 1/n convolutional code encoder can assist in searches for high-rate PCC encoders. On the other hand, we can derive a rate R = 1/n CC encoder from good PCC encoders with rate R = (n = 1)/n using dual code encoders. This paper proposes a method to obtain improved high-rate PCC encoders, using exhaustive search results of PCC encoders with rate R = 1/3 original encoders, and dual code encoders. We also show some PCC encoders obtained by searches that utilized our method.

关键词： convolutional code punctured code dual code weight spectrum

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