461 research outputs found
New Perturbed Proximal Point Algorithms for Set-valued Quasi Variational Inclusions
In this paper, by using some new and innovative techniques, some perturbed iterative
algorithms for solving generalized set-valued variational inclusions are suggested and
analyzed. Since the generalized set-valued variational inclusions include many variational
inclusions , variational inequalities and set-valued operator equation studied by others in
recent years, the results obtained in this paper continue to hold for them and represent a
significant refinement and improvement of the previously known results in this area
On Euclidean, Hermitian and symplectic quasi-cyclic complementary dual codes
Linear complementary dual codes (LCD) intersect trivially with their dual. In
this paper, we develop a new characterization for LCD codes, which allows us to
judge the complementary duality of linear codes from the codeword level.
Further, we determine the sufficient and necessary conditions for one-generator
quasi-cyclic codes to be LCD codes involving Euclidean, Hermitian, and
symplectic inner products. Finally, we constructed many Euclidean, Hermitian
and symmetric LCD codes with excellent parameters, some improving the results
in the literature. Remarkably, we construct a symplectic LCD code
with symplectic distance , which corresponds to an trace Hermitian additive
complementary dual code that outperforms the optimal quaternary
Hermitian LCD code
Improved Extreme Learning Machine and Its Application in Image Quality Assessment
Extreme learning machine (ELM) is a new class of single-hidden layer feedforward neural network (SLFN), which is simple in theory and fast in implementation. Zong et al. propose a weighted extreme learning machine for learning data with imbalanced class distribution, which maintains the advantages from original ELM. However, the current reported ELM and its improved version are only based on the empirical risk minimization principle, which may suffer from overfitting. To solve the overfitting troubles, in this paper, we incorporate the structural risk minimization principle into the (weighted) ELM, and propose a modified (weighted) extreme learning machine (M-ELM and M-WELM). Experimental results show that our proposed M-WELM outperforms the current reported extreme learning machine algorithm in image quality assessment
Symplectic self-orthogonal quasi-cyclic codes
In this paper, we obtain sufficient and necessary conditions for quasi-cyclic
codes with index even to be symplectic self-orthogonal. Then, we propose a
method for constructing symplectic self-orthogonal quasi-cyclic codes, which
allows arbitrary polynomials that coprime to construct symplectic
self-orthogonal codes. Moreover, by decomposing the space of quasi-cyclic
codes, we provide lower and upper bounds on the minimum symplectic distances of
a class of 1-generator quasi-cyclic codes and their symplectic dual codes.
Finally, we construct many binary symplectic self-orthogonal codes with
excellent parameters, corresponding to 117 record-breaking quantum codes,
improving Grassl's table (Bounds on the Minimum Distance of Quantum Codes.
http://www.codetables.de)
Some quaternary additive codes outperform linear counterparts
The additive codes may have better parameters than linear codes. However, it
is still a challenging problem to efficiently construct additive codes that
outperform linear codes, especially those with greater distances than linear
codes of the same lengths and dimensions. This paper focuses on constructing
additive codes that outperform linear codes based on quasi-cyclic codes and
combinatorial methods. Firstly, we propose a lower bound on the symplectic
distance of 1-generator quasi-cyclic codes of index even. Secondly, we get many
binary quasi-cyclic codes with large symplectic distances utilizing
computer-supported combination and search methods, all of which correspond to
good quaternary additive codes. Notably, some additive codes have greater
distances than best-known quaternary linear codes in Grassl's code table
(bounds on the minimum distance of quaternary linear codes
http://www.codetables.de) for the same lengths and dimensions. Moreover,
employing a combinatorial approach, we partially determine the parameters of
optimal quaternary additive 3.5-dimensional codes with lengths from to
. Finally, as an extension, we also construct some good additive
complementary dual codes with larger distances than the best-known quaternary
linear complementary dual codes in the literature
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