Configuration distribution and designs of codes in the Johnson scheme

The main goal of this article is to present several connections between perfect codes in the Johnson scheme and designs, and provide new tools for proving Delsarte conjecture that there are no nontrivial perfect Codes in the Johnson scheme. Three topics will be considered. The first is the configuration distribution which is akin to the weight distribution in the Hamming scheme. We prove that if there exists an e‐perfect code in the Johnson scheme then there is a formula which connects the number of vectors at distance i from any codeword in various codes isomorphic to . The second topic is the Steiner systems embedded in a perfect code. We prove a lower bound on the number of Steiner systems embedded in a perfect code. The last topic is the strength of a perfect code. We show two new methods for computing the strength of a perfect code and demonstrate them on 1‐perfect codes. We further discuss how to settle Delsarte conjecture. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 15–34, 2007     

关于Goppa 几何码最小距离的一个新方法

引进一个关于Goppa几何码(代数几何码)最小距离界的一个新方法.应用Maharaj的思想(即用显示基来近似表达Riemann-Roch空间)到Goppa几何码的最小距离的界上去.通过厄米特曲线上的代数几何码的一类例子,来证明标准的几何码的下界在某些情形下可以被显著地改进.进一步地,我们给出了这些码的最小距离上界,并说明了我们的下界非常接近这个上界.     

莫尔技术用于制作隐型全息密码的应用研究

提出根据莫尔理论制作隐型全息密码的方法,对此方法作了理论分析并给出实验结果。此方法有制作过程简单,所制作的密码隐蔽性高,检验密码方便的特点。有效地提高全息标识的防伪能力,因而具有很高的经济价值。     

平面曲线上几何MDS码的主猜想

本文用Ｌａｎｇ－Ｗｅｉｌ的一个经典结果证明了在一定维数限制下充分大域上平面代数曲线上ＭＤＳ码的主猜想成立。     

Mappings preserving spectrum and commutativity on Hermitian matrices

The general form of a continuous mapping φ acting on the real vector space of all n × n complex Hermitian or real symmetric matrices, and preserving spectrum and commutativity, is derived. It turns out that φ is either linear or its image forms a commutative set.     

Boron-doped a-SiOx:H films prepared by photo-CVD technique

The optoelectronic and structural properties of p-type a-SiO_x:H films have been studied. The deposition parameters e.g. chamber pressure and diborane to silane ratio are optimized to get a film with dark conductivity (σ_d) 7.9×10⁻⁶ S cm⁻¹ and photoconductivity 9.3×10⁻⁶ S cm⁻¹ for an optical gap (E₀₄) of 1.94 eV. The decrease of optical gap accompanied by the increase of conductivity is due to less oxygen incorporation in the film, which is substantiated by the decrease of the intensity of SiO absorption spectra. The properties are very much effected by the chamber pressure and diborane to silane ratio.     

Robust profilometer for the measurement of 3-D object shapes based on a regularized phase tracker

A robust profilometer is proposed to measure 3-D object shapes based on a regularized phase tracker that is capable of demodulating fringe patterns with a high noise presence and broad bandwidth due to the object shape. As shown herein, the technique acts as an adaptive filter and is capable of giving the detected phase continuously so that no further unwrapping process is required. Experimental results of real surface profiles are presented.     

Symmetry of the Riemann operator

Chaos quantization conditions, which relate the eigenvalues of a Hermitian operator (the Riemann operator) with the non-trivial zeros of the Riemann zeta function are considered, and their geometrical interpretation is discussed.     

Triaxial superdeformation in Lu

High-spin states in ¹⁶³Lu have been investigated using the Euroball spectrometer array. The previously known superdeformed band has been extended at low and high energies, and its connection to the normal-deformed states has been established. From its decay the mixing amplitude and interaction strength between superdeformed and normal states are derived. In addition, a new band with a similar dynamic moment of inertia has been found. The experimental results are compared to cranking calculations which suggest that the superdeformed bands in this mass region correspond to shapes with a pronounced triaxiality (γ≈±20°).     

An azo-isomerization-induced Freedericksz transition of a nematic liquid crystal

We observed an azo-isomerization-induced Freedericksz transition of the 5CB liquid crystal doped with 1% double-azo. In experiment, we found that the Freedericksz transition threshold occurred at optical intensity level of 0.3 mW/mm² for the 12.5 μm-thickness planar alignment doped 5CB, which is four orders of magnitude lower as that for the pure 5CB. Using optical phase retardation, we measured the relations between the Freedericksz transition threshold and the pump beam polarization. The maximum twist angle of liquid crystal molecules under different pump beam intensity is given. The experiment indicated that trans–cis isomerization plays an important role in the decrease of the Freedericksz transition threshold.