Pure Weierstrass gaps from a quotient of the Hermitian curve

Yang, Shudi; Hu, Chuangqiang

doi:10.1016/j.ffa.2017.12.002

Cited by 15 publications

(15 citation statements)

References 21 publications

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“…In Figure 2 we compare C 1 (r) in (17) and C 2 (r) in (18) for k = 20. Again r runs through 1 ≤ r ≤ q − 1 with q = 32 in this figure.…”

Section: Comparison Of the Boundsmentioning

confidence: 99%

“…Similarly Matthews [9] improved the bound on the minimum distance of the linear code if the support of G consists of two distinct points P 1 and P 2 using the Weierstrass semigorup of the pair (P 1 , P 2 ). Nowadays there are a lot of works devoted to further results on Weierstrass semigroups at several points on curves and their applications to coding theory (see, for example, [1], [2], [3], [18]).…”

Section: Introductionmentioning

confidence: 99%

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Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

2018

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“…In Figure 2 we compare C 1 (r) in (17) and C 2 (r) in (18) for k = 20. Again r runs through 1 ≤ r ≤ q − 1 with q = 32 in this figure.…”

Section: Comparison Of the Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

2018

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“…In [4] Carvalho and Torres consider in detail gaps and pure gaps at more than two places. Since then, pure gaps have been exhaustively studied to show that they provide many other good codes; see [2,5,20,23,25,29,30]. The scope of these papers varies depending on the algebraic curve and the number of places considered.…”

Section: Introductionmentioning

confidence: 99%

“…For those curves with affine equation given by y m = f (x) λ where m ≥ 2, λ ≥ 1 and f (x) is a separable polynomial over F q , general results on gaps and pure gaps can be found in [1,5,18,29]. Applications to codes on particular curves such as the Giulietti-Korchmáros curve, the Garcia-Güneri-Stichtenoth curve, and quotients of the Hermitian curve can be found in [19,28,31]. In [1] the authors use a decomposition of certain Riemann-Roch vector spaces due to Maharaj (Theorem 2.2) to describe gaps at one place arithmetically.…”

Section: Introductionmentioning

confidence: 99%

Pure gaps on curves with many rational places

Bartoli

Masuda

Montanucci

et al. 2018

Finite Fields and Their Applications

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“…Websites such as Kaggle plays a great role in promoting the semantic segmentation of images in practical applications and they are good at semantic editing or based on a more realistic scenario, such as MIT and satellite images, etc, for semantic segmentation in the context of deep learning. There are also a large number of valuable research results, which a large number of researchers have done semantic segmentation and realistic applications based on deep learning. Besides, the deep learning techniques have been applied to various fields of image processing such as other works, making a great breakthrough in traditional image processing.…”

Section: Introductionmentioning

confidence: 99%

Research of animals image semantic segmentation based on deep learning

Liu

et al. 2018

Concurrency and Computation

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It is imperative for us to develop the technology of image semantic segmentation with the increasing demand in the image processing. Nowadays, the development of deep learning is of great significance to the improvement of image segmentation. Furthermore, the paper discussed the relationship between image semantic segmentation and animal image research based on the actual situation, and found that animal image processing technology plays a more important role in the field of protecting precious animals. The end-to-end network training of this paper is consisted of Fully Convolutional Network (FCN) for the front end and Conditional Random Fields as Recurrent Neural Networks (CRF-RNN) for the back end via comparing a variety of research methods. The experiments achieved desired outcome for the semantic segmentation of animal images by utilizing Caffe deep learning framework and explained the implementation details from the aspects of training and testing. KEYWORDS Caffe, CRF-RNN, FCN, image semantic segmentation INTRODUCTIONTraditionally, the segmentation of the image is only directly on the surface layer, such as the appearance features based on texture, color, and shape, and they are separated after aggregating the similar features. Among them, the segmentation method based on regions, because the selection of seed points will lead to low efficiency of the algorithm, the segmented results have a certain flaw and can not reach the expected effect. However, the histogram-based threshold segmentation method ignores certain image space information, and it is very likely to segment a discontinuous and meaningless regions, making the segmentation result less satisfying. Therefore, with the demand for image segmentation technology, the semantic segmentation is indispensable.In semantic segmentation, the method of deep learning can be well escaped from the traditional processing methods, and the limitation of using only the underlying features is eliminated, making process in the level of understanding for image. The deep learning framework of Caffe 1 can handle semantic segmentation well. As the number of treasured animals continues to decline, the application of science and technology to protect them is imminent. In particular, it is necessary to collect a set of quality and distinctive animal image data for a specific animal, and the collection of a large number of data sets depends not only on human resources but also requires the support of the relevant sensors, cameras, and other hardware in the wild places it can automatically detect in the field or other places. One solution is to establish a corresponding index for the existing animal picture database. For the protected animal, it can use image processing technology to quickly identify for these animals, and then semantic segmentation is exploited to make a good recognition of animal images. This will not only increase the efficiency of the staff, but reduce the situation in which Concurrency Computat Pract Exper. 2020;32:e4892. wileyonlinelibrary.com/journal/cp...

show abstract

Pure Weierstrass gaps from a quotient of the Hermitian curve

Cited by 15 publications

References 21 publications

Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

Pure gaps on curves with many rational places

Research of animals image semantic segmentation based on deep learning

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