An A^3-code is extension of A^2-code in which none of the three participants： transmitter, receiver and arbiter, is assumed trusted. In this article, from projective geometry over finite fields, two A^3 -codes were g...An A^3-code is extension of A^2-code in which none of the three participants： transmitter, receiver and arbiter, is assumed trusted. In this article, from projective geometry over finite fields, two A^3 -codes were given, the parameters, and probabilities of successful attacks were computed.展开更多
Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of ...Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.展开更多
This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block co...This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.展开更多
The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and...The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).展开更多
The plane metrology using a single uncalibrated image is studied in the paper, and three novel approaches are proposed. The first approach, namely key-line-based method, is an improvement over the widely used key-poin...The plane metrology using a single uncalibrated image is studied in the paper, and three novel approaches are proposed. The first approach, namely key-line-based method, is an improvement over the widely used key-point-based method, which uses line correspondences directly to compute homography between the world plane and its image so as to increase the computational accuracy. The second and third approaches are both based on a pair of vanishing points from two orthogonal sets of parallel lines in the space plane together with two unparallel referential distances, but the two methods deal with the problem in different ways. One is from the algebraic viewpoint which first maps the image points to an affine space via a transformation constructed from the vanishing points, and then computes the metric distance according to the relationship between the affine space and the Euclidean space, while the other is from the geometrical viewpoint based on the invariance of cross ratios. The second and third methods avoid the selection of control points and are widely applicable. In addition, a brief description on how to retrieve other geometrical entities on the space plane, such as distance from a point to a line, angle formed by two lines, etc., is also presented in the paper. Extensive experiments on simulated data as well as on real images show that the first and the second approaches are of better precision and stronger robustness than the key-point-based one and the third one, since these two approaches are fundamentally based on line information.展开更多
The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective ...The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.展开更多
文摘An A^3-code is extension of A^2-code in which none of the three participants： transmitter, receiver and arbiter, is assumed trusted. In this article, from projective geometry over finite fields, two A^3 -codes were given, the parameters, and probabilities of successful attacks were computed.
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10371098 and the Natural Science Foundation of Shaanxi Province of ChinaIt is my pleasure to thank Prof. Qu Chang-Zheng for his helpful discussion
文摘Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.
基金the National Natural Science Foundation of China(No.60272009,No.60472045,and No.60496313).
文摘This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.
基金supported by The Norwegian Research Councilthe National Science Foundation of China(10271116)
文摘The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).
文摘The plane metrology using a single uncalibrated image is studied in the paper, and three novel approaches are proposed. The first approach, namely key-line-based method, is an improvement over the widely used key-point-based method, which uses line correspondences directly to compute homography between the world plane and its image so as to increase the computational accuracy. The second and third approaches are both based on a pair of vanishing points from two orthogonal sets of parallel lines in the space plane together with two unparallel referential distances, but the two methods deal with the problem in different ways. One is from the algebraic viewpoint which first maps the image points to an affine space via a transformation constructed from the vanishing points, and then computes the metric distance according to the relationship between the affine space and the Euclidean space, while the other is from the geometrical viewpoint based on the invariance of cross ratios. The second and third methods avoid the selection of control points and are widely applicable. In addition, a brief description on how to retrieve other geometrical entities on the space plane, such as distance from a point to a line, angle formed by two lines, etc., is also presented in the paper. Extensive experiments on simulated data as well as on real images show that the first and the second approaches are of better precision and stronger robustness than the key-point-based one and the third one, since these two approaches are fundamentally based on line information.
基金supported by the National Natural Science Foundation of China (Nos. 61303212 and 61170080)the State Key Program of the National Natural Science of China (Nos. 61332019 and U1135004)the Fundamental Research Funds for the Central Universities, South-Central University for Nationalities (No. CZY14019)
文摘The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.
