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On Isodual Double Toeplitz Codes

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Journal of Systems Science & Complexity 2024年第5期37卷 2196-2206页

作者： SHI Minjia XU Li solÉ patrick Key Laboratory of Intelligent Computing and Signal Processing Ministry of EducationSchool of Mathematical SciencesAnhui UniversityHefei 230601China State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China CNRS University of Aix MarseilleCentrale MarseilleI2MMarseille 13284France

Double Toeplitz(shortly DT)codes are introduced here as a generalization of double circulant *** authors show that such a code is isodual,hence formally self-dual(FSD).FSD codes form a far-reaching generalization of self-dual codes,the most important class of codes of rate ***-dual DT codes are characterized as double circulant or double ***,even binary DT codes are characterized as double *** examples obtained by exhaustive search show that the codes constructed have best-known minimum distance,up to one unit,amongst formally self-dual codes,and sometimes improve on the known *** q=2,the authors find four improvements on the best-known values of the minimum distance of FSD *** F4 an explicit construction of DT codes,based on quadratic residues in a prime field,performs equally *** authors show that DT codes are asymptotically good over ***,the authors construct DT codes arbitrarily close to the asymptotic Varshamov-Gilbert bound for codes of rate one half.

关键词： Double circulant codes double Toeplitz codes isodual codes formally self-dual codes

Two-Weight Codes and Second Order Recurrences

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Chinese Journal of Electronics 2019年第6期28卷 1127-1130页

作者： SHI Minjia ZHANG Zhongyi solé patrick Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Mathematical Sciences Anhui University School of Wendian Anhui University Aix Marseille Univ CNRS Centrale Marseile

Cyclic codes of dimension 2 over a finite field are shown to have at most two nonzero weights. We compute their weight distribution, and give a condition on the roots of their check polynomials for them to be maximum ... 详细信息

关键词： Two-weight codes Irreducible Cyclic codes MDS codes Linear recurrences

Optimal Ternary Cubic Two-Weight Codes

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Chinese Journal of Electronics 2018年第4期27卷 734-738页

作者： SHI Minjia HUANG Daitao sol patrick Key Laboratory of Intelligent Computing & Signal Processing Ministry of EducationAnhui University School of Mathematical Sciences Anhui University CNRS/LAGA University of Paris 8

We study trace codes with defining set L,a subgroup of the multiplicative group of an extension of degree m of a certain ring of order 27. These codes are abelian, and their ternary images are quasi-cyclic of coindex three(a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even. When m is odd, under some hypothesises on the size of L, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given.

关键词： Three-weight codes Two-weight codes Gauss sums Trace codes

Skew Cyclic Codes over a Non-chain Ring

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Chinese Journal of Electronics 2017年第3期26卷 544-547页

作者： SHI Minjia YAO Ting sol patrick Key Laboratory of Intelligent Computing & Signal Processing Ministry of Education Anhui University National Mobile Communications Research Laboratory Southeast University School of Mathematical Sciences of Anhui University CNRS/LAGA University of Paris 82 rue de la Libert93 526 Saint-Denis France

We study skew cyclic codes over a nonchain ring,which generalizes our previous results in IEICE *** Fundamentals of Electronic Communications and Computer Sciences,*** describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over the ring by a decomposition *** generator polynomial of the dual code of a skew cyclic code are ***,the idempotent generators of skew cyclic codes are *** examples are also presented to illustrate the discussed results.

关键词： Linear codes Gray map Dual codes Skew cyclic codes Generator polynomial

Self-Dual Hadamard Bent Sequences

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Journal of Systems Science & Complexity 2023年第2期36卷 894-908页

作者： SHI Minjia LI Yaya CHENG Wei CRNKOVIC Dean KROTOV Denis solépatrick Key Laboratory of Intelligent Computing Signal Processing Ministry of EducationSchool of Mathematical SciencesAnhui UniversityHefei 230601China State Key Laboratory of Information Security(Institute of Information Engineering) Chinese Academy of SciencesBeijing 100093China. LTCI Télécom ParisParis91120 PalaiseauFrance Secure-IC S.A.S. 104 Bd du Montparnasse75014 Paris Faculty of Mathematics University of RijekaNovosibirsk 630090Russia Sobolev Institute of Mathematics Novosibirsk 630090Russia Aix Marseille Univ CNRSCentrale MarseilleI2MMarseilleFrance

A new notion of bent sequence related to Hadamard matrices was introduced recently,motivated by a security application(solé,et al.,2021).The authors study the self-dual class in length at most *** authors use three competing methods of generation:Exhaustion,Linear Algebra and Gr?bner *** Hadamard matrices and Bush-type Hadamard matrices provide many *** authors conjecture that if v is an even perfect square,a self-dual bent sequence of length v always *** authors introduce the strong automorphism group of Hadamard matrices,which acts on their associated self-dual bent *** authors give an efficient algorithm to compute that group.

关键词： Bent sequences bush-type Hadamard matrices Hadanard matrices PUF functions regular Hadamard matrices

The Adjacency Codes of the First Yellow Graphs

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Journal of Systems Science & Complexity 2023年第4期36卷 1757-1768页

作者： SHI Minjia LI Shitao KIM Jon-Lark solE patrick Key Laboratory of Intelligent Computing and Signal Processing Ministry of EducationSchool of Mathematical SciencesAnhui UniversityHefei 230601China State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China School of Mathematical Sciences Anhui UniversityHefei 230026China Department of Math Sogang UniversitySeoulSouth Korea Aix Marseille Univ CNRSCentrale MarseilleI2MMarseilleFrance

The authors study the binary codes spanned by the adjacency matrices of the strongly regular graphs(SRGs)on at most two hundred vertices whose existence is *** authors show that in length less than one hundred they cannot be cyclic,except for the exceptions of the SRGs of parameters(85,42,20,21)and(96,60,38,36).In particular,the adjacency code of a(85,42,20,21)is the zero-sum *** the range[100,200]the authors find 29 SRGs that could possibly have a cyclic adjacency code.

关键词： Cyclic codes strongly regular graphs adjacency codes self-orthogonal codes

Human endogenous retrovirus type-W and multiple sclerosis–related smoldering neuroinflammation

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Neural Regeneration Research 2025年第3期20卷 813-814页

作者： Joel Gruchot Laura Reiche Andrew Chan Robert Hoepner patrick Küry Department of Neurology Medical Faculty and University Hospital DüsseldorfHeinrich Heine University DüsseldorfDüsseldorfGermany Department of Neurology InselspitalBern University Hospital and University of BernBernSwitzerland

Introduction to human endogenous retrovirus type-W(HERV-W): Genomic inheritance from the past includes retroviral sequences that have been stably incorporated into our genomes and account for up to 8% of human DNA.

关键词： endogenous inflammation Human

Smoothness of the Functional Law Generated by a Nonlinear SPDE

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Chinese Annals of Mathematics,Series B 2008年第2期29卷 113-120页

作者： Marta SANZ-sol Paul MALLIAVIN Facultat de Matemàtiques Universitat de BarcelonaGran Via 585E-08007 BarcelonaSpain. 10 rue Saint Louis-en-I'IleF-74004 ParisFrance

The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild *** is proved that the functional law of its solution is absolutely continuous and posses... 详细信息

关键词： Stochastic heat equation Probability law Absolute continuity Divergence operator Gradient operator

Microstructure and texture evolution of Ti-Nb-Si based alloys for biomedical applications

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Rare Metals 2006年第z2期25卷 163-167页

作者： KIM Won-Yong KIM Han-sol Advanced Materials R&D Division Korea Institute of Industrial Technology Incheon 406-130 Korea

Microstructure and texture of Ti-Nb-Si based alloys, prepared by water quenching from β-phase field, cold rolling and recrystallization heat treatment followed by water quenching, were investigated in terms of optical microstructure and analysis of X-ray pole figure result. In as-quenched sample, relatively random distribution of pole figure was detected without showing a specific texture component. In as-cold rolled sample, however, it is found well-developed several texture components consisting of rotated cube, α-fiber and γ-fiber texture components which are frequently observed in bcc-structured metals and alloys were found. Therefore, texture components developed in the present alloys are closely related to the deformation of β-phase even though small amount of α″ phase co-exist in the microstructure. In recrystallized sample, α-fiber texture component is weakly detected while the other texture components, rotated cube and γ-fiber components, appears to be relatively unchanged. No additional texture components were detected besides those texture components observed in the cold rolled samples.

关键词： Ti-Nb-Si based alloys microstructure texture