Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

Picosecond Laser Machining of Deep Holes in Silicon Infiltrated Silicon Carbide Ceramics

Silicon infiltrated silicon carbide （Si-SiC） ceramics, as high hardness materials, are difficult to machine, especially drilling micro-holes. In this study, the interaction of picosecond laser pulses （1 ps at 1 030 nm） with Si-SiC ceramics was investigated. Variations of the diameter and depth of circular holes with the growth of the laser energy density were obtained. The results indicate that the increase of machining depth follows a nonlinear relation with the increasing of laser energy density, while the diameter has little change with that. Moreover, it is found that some debris and particles are deposited around and inside the holes and waviness is in the entrance and at walls of the holes after laser processing.

On Deep Holes of Projective Reed-Solomon Codes over Finite Fields with Even Characteristic

Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding.In this paper,we obtain two classes of deep holes of projective Reed-Solomon codes over finite fields with even characteristic.That is,let F_(q) be finite field with even characteristic,k∈{2,q-2},and let u(x)be the Lagrange interpolation polynomial of the first q components of the received vector u∈F_(q)+1 q Suppose that the(q+1)-th component of u is 0,and u(x)=λx^(k)+f_(≤k-2)(x),λx^(q-2)+f_(≤k-2)(x),where λ∈F^(*)_(q) and f_(≤k-2)(x)is a polynomial over F_(q) with degree no more than k-2.Then the received vector u is a deep hole of projective Reed-Solomon codes PRS(F_(q),k).In fact,our result partially solved an open problem on deep holes of projective Reed-Solomon codes proposed by Wan in 2020.

Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We then study the deep hole problem of generalized Reed-Solomon (RS) codes over finite local rings. Several different classes of deep holes are constructed. The relationship between finite geometry and deep holes of RS codes over finite local rings are also studied.

Theoretical and numerical simulation investigation of deep hole dispersed charge cut blasting

Drilling and blasting methods have been used as a common driving technique for shallow-hole driving and blasting in rock roadways.With the advent of digital electronic detonators and the need for increased production efciency,the traditional blasting design is no longer suitable for deep hole blasting.In this paper,a disperse charge cut blasting method was proposed to address the issues of low excavation depth and high block rate in deep hole undercut blasting.First,a blasting model was used to illustrate the mechanism of the deep hole dispersive charge cut blasting process.Then,continuous charge and dispersed charge blasting models were developed using the smooth particle hydrodynamics-fnite element method(SPHFEM).The cutting parameters were determined theoretically,and the cutting efciency was introduced to evaluate the cutting efect.The blasting efects of the two charging models were analyzed utilizing the evolution law of rock damage,the number of rock particles thrown,and the cutting efciency.The results show that using a dispersed charge improves the cutting efciency by about 20%and the rock breakage for the deep hole cut blasting compared to the traditional continuous charge.In addition,important parameters such as cutting hole spacing,cutting hole depth and upper charge proportion also have a signifcant impact on the cutting efect.Finally,the deep hole dispersed charge cut blasting technology is combined with the digital electronic detonator through the feld engineering practice.It provides a reference for the subsequent deep hole cutting blasting and the use of electronic detonators in rock roadways.

Heptad Phase Vortex Array in Extremely Deep Fresnel Diffraction Region Generated by Asymmetrical Metal Subwavelength Holes Film

We report a heptad vortex array structure in the wave fields in an extremely deep Fresnel diffraction region by asymmetrical subwavelength holes in a metal film illuminated with linearly polarized light. A Mach Zehnder interferometer with a microscopic objective is used to record the wave fields at different distance＆ and the phase maps are extracted by Fourier transform of the interference intensities. We study the evolutions of the heptad vortex array with distance from the sample to the object plane. To explain the formations and the evolutions of the vortex array, we calculate the diffracted wave fields with Kirchhoff＇s diffraction theory. The calculations are basically consistent with the experimental results, and the properties of the heptad vortex array structure are reasonably explained.

Investigation of etching method for fabricating deep through holes on ultra-high resistivity silicon

In this paper,the etching characteristics of the ultra-high resistivity silicon（UHRS） by using the Bosch process were investigated.The experimental results indicated that the sulfur hexafluoride flux,the temperature of the substrate,the platen power and the etching intermittence had important influence on the etching rate and the etching morphology of the UHRS.The profiles and morphologies of sidewall were characterized with scanning electron microscopy（SEM）.By using an improved three-stage Bosch process,380-μm deep through holes were fabricated on the UHRS with the average etching rate of about 3.14 μm/min.Meanwhile,the fabrication mechanism of deep through holes on the UHRS by using the three-stage Bosch process was illustrated on the basis of the experimental results.

Experimental and computational analysis of the coolant distribution considering the viscosity of the cutting fluid during machining with helical deep hole drills

An experimental analysis regarding the distribution of the cutting fluid is very difficult due to the inaccessibility of the contact zone within the bore hole.Therefore,suitable simulation models are necessary to evaluate new tool designs and optimize drilling processes.In this paper the coolant distribution during helical deep hole drilling is analyzed with high-speed microscopy.Micro particles are added to the cutting fluid circuit bya developed high-pressure mixing vessel.After the evaluation of suitable particle size,particle concentration and coolant pressure,a computational fluid dynamics(CFD)simulation is validated with the experimental results.The comparison shows a very good model quality with a marginal difference for the flow velocity of 1.57%between simulation and experiment.The simulation considers the kinematic viscosity of the fluid.The results show that the fluid velocity in the chip flutes is low compared to the fluid velocity at the exit of the coolant channels of the tool and drops even further between theguidechamfers.Theflow velocity and the flow pressure directly at the cutting edge decrease to such an extent that the fluid cannot generate a sufficient cooling or lubrication.With the CFD simulation a deeper understanding of the behavior and interactions of the cutting fluid is achieved.Based on these results further research activities to improve the coolant supply can be carried out with great potential to evaluate new tool geometries and optimize the machining process.