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Linear recurring sequences and subfield subcodes of cyclic codes

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Science China Mathematics 2013年第7期56卷 1413-1420页

作者： GAO ZhiHan fu fangwei Department of Combinatorics and Optimization University of Waterloo Chern Institute of Mathematics and LPMC Nankai University

Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .

关键词： linear recurring sequences characteristic polynomial cyclic codes subfield subcodes trace codes

Construction of compressed sensing matrices based on affine symplectic space over finite fields

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The Journal of China Universities of Posts and Telecommunications 2018年第6期25卷 74-80页

作者： Wang Gang Niu Minyao fu fangwei Chern Institute of Mathematics and Lab of Pure Mathematics and Combinatorics Nankai University College of Science Civil Aviation University of China

The compressed sensing matrices based on affine symplectic space are constructed. Meanwhile, a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. Moreover, we merge our binary matrices with other low coherence matrices such as Hadamard matrices and discrete fourier transform(DFT) matrices using the embedding operation. In the numerical simulations, our matrices and modified matrices are superior to Gaussian matrices and DeVore’s matrices in the performance of recovering original signals.

关键词： compressed sensing coherence sparsity affine symplectic space finite fields

The existence and synchronization properties of symmetric fix-free codes

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Science China(Information Sciences) 2013年第9期56卷 240-248页

作者： GUANG Xuan fu fangwei CHEN LuSheng Chern Institute of Mathematics and LPMC Nankai University School of Mathematical Science Nankai University

Fix-free codes are a type of variable length codes with both prefix-free and suffix-free properties, and there are two types of fix-free codes: symmetric fix-free codes and asymmetric fix-free codes. In this paper, we mainly discuss symmetric fix-free codes. First, the existence of symmetric fix-free codes is studied in detail, and some necessary and sufficient conditions are proposed. We also discuss the problem of achieving synchronization of symmetric fix-free codes, which is important in application. We then establish a scheme with synchronizing codewords to resolve this problem.

关键词： fix-free codes RVLCs symmetric codes synchronization source encoding data compression

Hypothesis Testing for Arbitrarily Varying Source

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Acta Mathematica Sinica,English Series 1996年第1期12卷 33-39页

作者： fu fangwei Shen Shiyi Department of Mathematics Nankai University Tianjin, 300071 China Department of Mathematics Nankai University Tianjin China

Hypothesis testing for arbitrarily varying source (AVS), which is to decide between the two hypotheses for the varying behavior of the distribution of AVS, is considered in this paper. We determine the best asymptotic exponent of the second kind of error probability when the first kind of error probability is fixed. This result generalizes the well-known lemma of Stein in statistics. As a corollary, Strassen’s coding theorem for AVS is obtained.

关键词： Hypothesis testing Stein lemma Arbitrarily varying source Coding theorem

STRONG CODING THEOREM AND ASYMPTOTICERROR EXPONENT OF ARBITRARILY VARYING SOURCE WITH A FIDELITY CRITERION

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Systems Science and Mathematical Sciences 1998年第2期11卷 168-174页

作者： fu fangwei SHEN Shiyi(Department Of Mathematics, Nankai University, Tiawtn 300071, China)

When the error probability is less than 2--"", the minimum compression rate(r-optimal rate) of arbitrarily varying source with a fidelity criterion is determined. Thisgeneralizes the result of Arutyunyan and Mekaushll] for discrete memoryless source witha fidelity criterion, and is called strong coding theorem of arbitrarily varying source witha fidelity criterion. We also determine the asymptotic error exponellt for arbitrarily varying source with a fidelity criterion. This generalizes Marton’s result in [2] for discretememoryless source with a fidelity criterion.

关键词： Arbitrarily varying sourcel coding theorem error exponent information quantity rate-distortion theory.

Correlations and stoichiometric characteristics of C,N,and P contents in Juniperus saltuaria plants,litter,and soil in the Sygera Mountains,southeastern Xizang,China

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Journal of Mountain Science 2024年第12期21卷 4254-4268页

作者： GUO Liangna LI Jiangrong fu fangwei ZHANG Bo ZHU Sijie LIU Yuzhuo LI Jieting CHEN Ganggang ZHANG Yibo Research Institute of Tibet Plateau Ecology Tibet Agricultual&Animal Husbandry UniversityNyingchi 860000China Key Laboratory of Forest Ecology in Tibet Plateau Ministry of EducationNyingchi 860000China National Key Station of Field Scientific Observation&Experiment Nyingchi 860000China Key Laboratory of Alpine Vegetation Ecological Security in Tibet Nyingchi 860000China

Research on the multicomponent synergistic relationships between plants,litter,and soil from the perspective of ecological stoichiometry helps to understand nutrient cycling and distribution mechanisms within *** study focused on Juniperus saltuaria,the dominant tree species in the forestline ecotone of Sygera Mountains,southeastern Xizang,*** systematically measured and analyzed the Carbon(C),nitrogen(N),and phosphorus(P)contents and their relationships in plants(leaves,branches,trunks,fine roots),litter(undecomposed layer,partially decomposed layer,fully decomposed layer),and soil(0-10 cm,10-20 cm,20-40 cm)at different slope *** results showed significant differences in the C,N,and P contents and stoichiometry of plants and soil at different slope positions,while no significant differences were observed among litter *** the same slope position,the C,N,and P contents in leaves and surface soil were the highest,with soil nutrients significantly decreasing with increasing *** litter,the C content in the undecomposed layer was significantly higher than that in the partially and fully decomposed layers while the P content showed the opposite *** soil(0-20 cm)exhibited a decoupled relationship with plants but a coupled relationship with litter while deep soil(20-40 cm)showed a coupled relationship with *** showed faster growth rates on uphill *** this study area,*** exhibited consistent trends of N,P,and N:P ratios homeostasis across different slope positions and organs,with leaves and fine roots both limited by *** interactive effects between plants,litter,and soil nutrients were observed across different slope *** correlations were found between leaf and litter,and between fine root and leaf while the relationships between litter and soil,and between soil and fine root,*** study helps improve our understanding of the nutrient interactions between plants,litter

关键词： Leaf-litter-soil system Slope position C:N:P stoichiometry Forestline ecotone Nutritional restriction Juniperus saltuaria

ON THE MEAN VALUE AND VARIANCE OF DISTANCE DISTRIBUTION OF NON-LINEAR CODES IN GF(q)

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Journal of Electronics(China) 1998年第1期15卷 58-62页

作者： fu fangwei Shen Shiyi(Department of Mathematics, Nankai University, Tianjin 300071) Department of Mathematics Nankai University Tianjin

This paper presents the lower bounds and upper bounds for the mean value and variance of distance distribution of non-linear codes in GF(q). By presenting several examples, it is shown that these bounds could be achie... 详细信息

关键词： Coding theory Distance distribution Althofer-Sillke inequality MacWilliams-Delsarte identity