Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal...Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.展开更多
In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the ...In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.展开更多
Recognition of human gesture actions is a challenging issue due to the complex patterns in both visual andskeletal features. Existing gesture action recognition (GAR) methods typically analyze visual and skeletal data...Recognition of human gesture actions is a challenging issue due to the complex patterns in both visual andskeletal features. Existing gesture action recognition (GAR) methods typically analyze visual and skeletal data,failing to meet the demands of various scenarios. Furthermore, multi-modal approaches lack the versatility toefficiently process both uniformand disparate input patterns.Thus, in this paper, an attention-enhanced pseudo-3Dresidual model is proposed to address the GAR problem, called HgaNets. This model comprises two independentcomponents designed formodeling visual RGB (red, green and blue) images and 3Dskeletal heatmaps, respectively.More specifically, each component consists of two main parts: 1) a multi-dimensional attention module forcapturing important spatial, temporal and feature information in human gestures;2) a spatiotemporal convolutionmodule that utilizes pseudo-3D residual convolution to characterize spatiotemporal features of gestures. Then,the output weights of the two components are fused to generate the recognition results. Finally, we conductedexperiments on four datasets to assess the efficiency of the proposed model. The results show that the accuracy onfour datasets reaches 85.40%, 91.91%, 94.70%, and 95.30%, respectively, as well as the inference time is 0.54 s andthe parameters is 2.74M. These findings highlight that the proposed model outperforms other existing approachesin terms of recognition accuracy.展开更多
文摘Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.
文摘In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.
基金the National Natural Science Foundation of China under Grant No.62072255.
文摘Recognition of human gesture actions is a challenging issue due to the complex patterns in both visual andskeletal features. Existing gesture action recognition (GAR) methods typically analyze visual and skeletal data,failing to meet the demands of various scenarios. Furthermore, multi-modal approaches lack the versatility toefficiently process both uniformand disparate input patterns.Thus, in this paper, an attention-enhanced pseudo-3Dresidual model is proposed to address the GAR problem, called HgaNets. This model comprises two independentcomponents designed formodeling visual RGB (red, green and blue) images and 3Dskeletal heatmaps, respectively.More specifically, each component consists of two main parts: 1) a multi-dimensional attention module forcapturing important spatial, temporal and feature information in human gestures;2) a spatiotemporal convolutionmodule that utilizes pseudo-3D residual convolution to characterize spatiotemporal features of gestures. Then,the output weights of the two components are fused to generate the recognition results. Finally, we conductedexperiments on four datasets to assess the efficiency of the proposed model. The results show that the accuracy onfour datasets reaches 85.40%, 91.91%, 94.70%, and 95.30%, respectively, as well as the inference time is 0.54 s andthe parameters is 2.74M. These findings highlight that the proposed model outperforms other existing approachesin terms of recognition accuracy.
