Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes that are MDS yet not generalized Reed-Solomon codes, called non-generalized Reed-Solomon MDS codes, started with the work by Roth and Lemple (1989), where the first examples were exhibited. It then gained traction thanks to the work by Beelen et al. (2017), who introduced twisted Reed-Solomon codes, and showed that families of such codes are non-generalized Reed-Solomon MDS codes. Finding non-generalized Reed-Solomon MDS codes is naturally motivated by the classification of MDS codes. In this paper, we provide a generic construction of MDS codes, yielding infinitely many examples. We then explicit families of non-generalized Reed-Solomon MDS codes. Finally we position some of the proposed codes with respect to generalized twisted Reed-Solomon codes, and provide new view points on this family of codes.

Cloud computing has revolutionized data center management by providing scalable and efficient resources for processing and data management. However, deploying containerd-based services in data centers presents significant challenges: (1) Active servers that are underutilized result in high energy consumption, necessitating optimization for energy efficiency; (2) Affinity requirements between services and servers must be considered to ensure appropriate deployments; (3) Quality of Service (QoS) requirements must be met, particularly to avoid performance interference when multiple services are deployed on the same server. To address these challenges, we propose a novel algorithm, Affinity-Interference Energy Deployment (AIED), based on Deep Reinforcement Learning (DRL). This algorithm strategically consolidates services onto fewer servers to optimize energy efficiency while adhering to stringent QoS and affinity constraints. By employing a demand-supply model to quantify QoS requirements and formulating the deployment challenge as a Markov Decision Process (MDP), our algorithm dynamically adapts to fluctuating demands and resource availability. Extensive simulations demonstrate that AIED significantly outperforms existing baseline strategies, reducing energy consumption while ensuring robust compliance with both QoS and affinity constraints.

Abstract The Rankin constant $$\gamma _{n,l}$$ γ n , l measures the largest volume of the densest sublattice of rank l of a lattice $$\Lambda \in {\mathbb {R}}^n$$ Λ ∈ R n over all such lattices of rank n. The Bergé-Martinet constant $$\gamma '_{n,l}$$ γ n , l ′ is a variation that takes into account the dual lattice. Exact values and bounds for both constants are mostly open in general. We consider the case of lattices built from linear codes, and look at bounds on $$\gamma _{n,l}$$ γ n , l and $$\gamma '_{n,l}$$ γ n , l ′ . In particular, we revisit known results for $$n=3,4,5,8$$ n = 3 , 4 , 5 , 8 and give lower and upper bounds for the open cases $$\gamma _{5,2},\gamma _{7,2}$$ γ 5 , 2 , γ 7 , 2 and $$\gamma '_{5,2},\gamma '_{7,2}$$ γ 5 , 2 ′ , γ 7 , 2 ′ .

Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight$\left [{{\frac {q^{k}-1}{q-1},k,q^{k-1}}}\right ]_{q}$-linear codes and they meet all Griesmer bounds on the generalized Hamming weights of linear codes. All the subcodes with dimension r of a$\left [{{\frac {q^{k}-1}{q-1},k,q^{k-1}}}\right ]_{q}$-simplex code have the same subcode support weight$\frac {q^{k-r}(q^{r}-1)}{q-1}$for$1\leq r\leq k$. In this paper, we construct linear codes meeting the Griesmer bound of the r-generalized Hamming weight, such codes do not meet the Griesmer bound of the j-generalized Hamming weight for$1\leq j\lt r$. Moreover these codes have only few subcode support weights (few-SSW). The weight distributions and the subcode support weight distributions of these distance-optimal codes are determined. Linear codes constructed in this paper are natural generalizations of distance-optimal few-weight codes.

Autonomous Underwater Vehicle (AUV) with towed Magnetic Anomaly Detection (MAD) system is a reliable technique for detecting underwater magnetic targets. However, arranging too many magnetometers in the towed MAD system is not suitable, and the key lies in their reasonable arrangement. As a result, this paper proposes a new MAD system equipped with two scalar and one vector magnetometers, along with the corresponding multi-parameter magnetic target localization method. By using two scalar magnetometers and the geometric relationship with vector magnetometer, the time when the vector magnetometer reaches the closest point approach (CPA) on the trajectory and the value range of the shortest distance are obtained. The value range of the shortest distance is cleverly set as the search boundary for the improved particle swarm optimization algorithm in this dimension, which greatly mitigates the randomness of the optimization algorithm and enhances the accuracy of the solution. Subsequently, the unique solution for the magnetic target parameters can be easily obtained by using the vector magnetometer. The combination of scalar and vector magnetometers proves to be both economical and effective. Numerical simulation and field experiments show that this method provides a new idea for static magnetic target detection.

In order to verify the supplementary effect of radar remote sensing on optical remote sensing in geological applications, an experimental study on the use of fully polarimetric radar data for lithologic classification is carried out. First, the ASTER data are used to classify the lithology, and then the ASTER and RadarSAT-2 data are superimposed on the lithology classification, and the results are quantitatively evaluated by the existing regional geological survey map. The results show that the total polarization SAR images can be superimposed on the optical images, which can effectively improve the accuracy of lithologic classification.

By identifying temporarily stable natural reflectors or persistent scatterers (PS), PSInSAR (Persistent Scatterers for SAR Interferometry) technique can analyze this subset of pixels in SAR images, even with long temporal and space baselines, to get high accuracy deformation measurements. We implement the PSInSAR process that is briefly summarized in this paper and apply this method in Tianjin area to detect the deformation phenomena using ENVISAT ASAR images. Calibration of ASAR images helps us select more PSC and using calibrated backscattering coefficient threshold we can discard the pixels whose amplitude are relatively stable while whose backscattered signals are weak and incoherent. Results obtained by processing 14 images show the distribution and the relative deformation value of the displacement field. The estimated linear velocities of PS are not accurate enough because of the relatively small number of images.