环 F2＋ uF2＋ u2 F2上的常循环码

常循环码是一类重要的纠错码,本文基于（xn －1）在 F2[x]上的分解,探讨了环 R＝ F2＋ uF2＋ u2 F2上任意长度的（1＋λu）常循环码的极小生成元集（λ为R上的单位）。通过分析该环上循环码和常循环码的置换等价性,得到了该环上码长为奇数及码长 N≡2（mod 4）时（1＋ u2）常循环码的生成多项式和极小生成元集。     

环Z2m上一类常循环码的挠码及其应用

该文研究了环Z_2^m上任意长的（1+2λ）-常循环码的挠码及其应用.首先,给出环Z_2^m上（1+2λ）-常循环码的挠码.然后,利用挠码得到环Z_2^m上某些（1+2λ）-常循环码的齐次距离分布.同时,利用挠码证明了环Z_2^m上（2^m－1－1）-常循环自对偶码都是类型I码,并利用这类码构造了极优的类型I码.     

环Ｆ2+uＦ2上长为2e的循环码

近十多年来,有限环上的循环码一直是编码研究者所关心的热点问题,本文证明了R[x]/＜xn-1＞不是主理想环,其中R=F2 uF2,u2=0且n=2e.分3种情形讨论了环R[x]/＜xn-1＞中的非零理想,并给出了R上循环码的可以唯一确定的生成元的表达形式,同时给出了R上循环码的李距离的一个上界估计.     

环F2+uF2上长度为2e的循环码的距离

确定码字的Hamming距离和Lee距离是解码的关键.本文对环F₂+uF₂上长度为2^e的循环码的结构进行了分类.确定了环F₂+uF₂上某些长度为2^e的循环码的Hamming距离和Lee距离.给出了环F₂+uF₂上长度为2^e的其它循环码的Hamming距离的上界及Lee距离的上界和下界.     

Ca3(BO3)2的振动光谱分析

分别利用因子群对称分析法和位置群对称分析法对Ca₃(BO₃)₂晶体的振动模式进行了理论分析。Ca₃(BO₃)₂的晶格振动模式分为外振动和内振动模式,外振动模式为:3A_1g+4A_2g+7E_g+3A_1u+3A_2u+6E_u,内振动模式为：2A_1g+2A_2g+4E_g+2A_1u+2A_2u+4E_u。Ca₃(BO₃)₂晶体在布里渊区中心Γ点晶格振动的对称性分类为：5A_1g+6A_2g+11E_g+5A_1u+6A_2u+11E_u,其中声学模为：A_2u+E_u,拉曼活性光学模为5A_1g+11E_g,红外活性光学模为：5A_2u+10E_u,其余为非拉曼、非红外活性光学振动模。用高温固相法成功合成了Ca₃(BO₃)₂粉末,测量了它的室温Raman光谱,并利用群论分析的结果对谱图进行了讨论,指认了BO₃^3-基团的特征振动频率。     

Ti3C2/N-TiO2复合材料的制备及吸附/光催化去除污染物性能

首先利用煅烧TiN制备了N-TiO₂,并采用HF溶液腐蚀Ti₃AlC₂合成了Ti₃C₂,然后将两者以不同质量比值进行混合,通过超声法构建了一系列Ti₃C₂/N-TiO₂复合材料。采用X射线衍射仪、透射电子显微镜、X射线光电子能谱仪、紫外-可见分光光度计等多种表征手段对样品的物相、形貌和组成进行了分析。以罗丹明B水溶液为模拟污染物,研究了样品对污染物的吸附性能和光催化降解性能。结果表明,6%Ti₃C₂/N-TiO₂复合材料显示出最好的污染物吸附性能和可见光光催化降解性能,其光催化降解污染物效率分别是10%Ti₃C₂/N-TiO₂、2%Ti₃C₂/N-TiO₂和N-TiO₂的1.2、1.4和1.9倍。...     

NiS/TiO2/Ti3C2三元异质结结构的构筑及光催化产氢性能

二维过渡金属碳化物MXene(Ti₃C₂)因其优良二维层状结构及导电性被认为是一种理想的光催化材料。采用两步水热法结合原位自氧化方法合成了NiS/TiO₂/Ti₃C₂(TCTNS)三元复合光催化剂。运用多种分析手段(场发射扫描电子显微镜(FESEM)、X射线衍射仪(XRD)、紫外-可见光(UV-Vis)吸收光谱仪及光电流测试)对其结构进行了表征,研究了其光催化分解水产氢的活性,探讨了材料的组成、结构与性能之间的相互影响。结果表明,与单一NiS和二元TiO₂/Ti₃C₂催化剂相比,复合光催化剂具有更高的光电性能。其可见光驱动的光催化H₂产氢速率可达3 269μmol/(g·h),是二元TiO₂/Ti₃C₂产氢速率的约19倍。实验结果表明,由于NiS和TiO₂纳米颗粒覆盖重建的多异质结界面,以及TCTNS复合...     

不同退火氛围对TiN/HfO2/SiO2/Si结构电荷分布的影响

热退火技术是集成电路制造过程中用来改善材料性能的重要手段。系统分析了两种不同的退火条件(氨气氛围和氧气氛围)对TiN/HfO₂/SiO₂/Si结构中电荷分布的影响,给出了不同退火条件下SiO₂/Si和HfO₂/SiO₂界面的界面电荷密度、HfO₂的体电荷密度以及HfO₂/SiO₂界面的界面偶极子的数值。研究结果表明,在氨气和氧气氛围中退火会使HfO₂/SiO₂界面的界面电荷密度减小、界面偶极子增加,而SiO₂/Si界面的界面电荷密度几乎不受退火影响。最后研究了不同退火氛围对电容平带电压的影响,发现两种不同的退火条件都会导致TiN/HfO₂/SiO₂/Si电容结构平带电压的正向漂移,基于退火对其电荷分布的影响研究,此正向漂移主要来源于退火导致的HfO₂/SiO₂界面的界面偶极子的增加。     

WO3/SnO2复合薄膜的制备及光电性能

采用水热法和电化学沉积法,成功制备了包覆有SnO₂纳米颗粒的WO₃纳米棒阵列薄膜,退火处理后形成WO₃/SnO₂异质结复合薄膜。通过改变SnO₂的沉积时间得到了复合薄膜的最佳制备条件。采用XRD,FESEM对WO₃/SnO₂复合薄膜的物相和形貌进行了分析,通过电化学工作站对WO₃/SnO₂复合薄膜的光电性能进行了研究,结果表明,电沉积时间为120 s时,WO₃/SnO₂复合薄膜具有最小的阻抗,且在0.6 V的偏压下光电流密度为0.46 mA/cm²,相比于单一WO₃纳米棒薄膜,表现出更好的光电化学性能。     

B2O3对BaZrO3微波介质陶瓷材料性能的影响

以分析纯的BaCO₃、ZrO₂、B₂O₃为原料,采用传统固相法制备了添加x%B₂O₃(质量分数x=0.5～5.0)的BaZrO₃微波介质陶瓷。运用扫描电子显微镜、矢量网络分析仪和X线衍射仪等实验手段研究了不同B₂O₃添加量对BaZrO₃陶瓷微观结构、相组成及微波介电性能的影响。结果表明,随着B₂O₃添加量的增加,材料致密烧结温度降低,介电常数减小,介电损耗降低。当B₂O₃添加量超过1%时,有BaZr(BO₃)₂相析出。在B₂O₃添加量为3%,烧结温度为1 300℃时,BaZrO₃陶瓷获得优异的微波介电性能：介电常数ε_r=33.02,品质因数与频率之积Q×...     

Cyclic codes and self-dual codes over F2+uF2

We introduce linear cyclic codes over the ring F₂+uF ₂={0,1,u,u¯=u+1}, where u²=0 and study them by analogy with the Z₄ case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z₄-codes. Unlike the Z₄ case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map     

Algebraic construction of cyclic codes over Z8 with agood Euclidean minimum distance

Let S(8) denote the set of the eight admissible signals of an 8PSK communication system. The alphabet S(8) is endowed with the structure of Z₈, the set of integers taken modulo 8, and codes are defined to be Z₈-submodules of Z₈ⁿ. Three cyclic codes over Z₈ are then constructed. Their length is equal to 6, 8, and 7, and they, respectively, contain 64, 64, and 512 codewords. The square of their Euclidean minimum distance is equal to 8, 16-4√2 and 10-2√2, respectively. The size of the codes of length 6 and 7 can be doubled while the Euclidean minimum distance remains the same     

On coset weight distributions of the Z4-linear Goethalscodes

We study the coset weight distributions of two well-known families of codes: the three-error-correcting binary Z₄-linear Goethals codes of length N=2^m+1, m⩾3 odd, and the Z₄ -linear Goethals codes over Z₄ of length n=N/2=2^m . The hard case is the weight distributions of cosets of weight 4. To know the weight distribution of the coset of weight 4 we have to know the number of codewords of weight 4 in such a coset. Altogether, there are nine different types of cosets of weight 4. For six cases, we give the exact expressions for the number of codewords of weight 4, and for three other cases, we give such expressions in terms of Kloosterman sums     

Cyclic codes over Z4, locator polynomials, and Newton'sidentities

Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock (1972) and Preparata (1968) codes that can be very simply constructed as binary images, under the Gray map, of linear codes over Z₄ that are defined by means of parity checks involving Galois rings. This paper describes how Fourier transforms on Galois rings and elementary symmetric functions can be used to derive lower bounds on the minimum distance of such codes. These methods and techniques from algebraic geometry are applied to find the exact minimum distance of a family of Z ₄. Linear codes with length 2^m (m, odd) and size 2(2^m+1-5m-2). The Gray image of the code of length 32 is the best (64, 2³⁷) code that is presently known. This paper also determines the exact minimum Lee distance of the linear codes over Z₄ that are obtained from the extended binary two- and three-error-correcting BCH codes by Hensel lifting. The Gray image of the Hensel lift of the three-error-correcting BCH code of length 32 is the best (64, 2³²) code that is presently known. This code also determines an extremal 32-dimensional even unimodular lattice     

Further results on generalized Hamming weights for Goethals andPreparata codes over Z4

This article contains results on the generalized Hamming weights (GHW) for the Goethals and Preparata codes over Z₄. We give an upper bound on the rth generalized Hamming weights d_r(m,j) for the Goethals code G_m(j) of length 2^m over Z ₄, when m is odd. We also determine d_3.5(m,j) exactly. The upper bound is shown to be tight up to r=3.5. Furthermore, we determine the rth generalized Hamming weight d_r(m) for the Preparata code of length 2^m over Z₄ when r=3.5 and r=4     

An Assmus-Mattson theorem for Z4-codes

The Assmus-Mattson theorem is a method to find designs in linear codes over a finite field. The purpose of this paper is to give an analog of this theorem for Z₄-codes by using the harmonic weight enumerator introduced by Bachoc. This theorem can find some 5-designs in the lifted Golay code over Z₄ which were discovered previously by other methods     

有限非链环Fpm+vFpm上循环码的迹码和子环子码

给出了有限非链环F_p^m+vF_p^m的Galois扩环相关理论,明确了有限非链环F_p^m+vF_p^m上循环码的迹码和子环子码的生成元结构.     

Translates of linear codes over Z4

We give a method to compute the complete weight distribution of translates of linear codes over Z₄. The method follows known ideas that have already been used successfully by others for Hamming weight distributions. For the particular case of quaternary Preparata codes, we obtain that the number of distinct complete weights for the dual Preparata codes and the number of distinct complete coset weight enumerators for the Preparata codes are both equal to ten, independent of the code length     

环F2+uF2+…+uk-1F2上常循环自对偶码

最近,剩余类环上的常循环码及常循环自对偶码引起了编码学者的极大关注.本文首先利用一些相关的线性码,建立了一类特殊有限链环上长为N的常循环自对偶码的一般理论,利用其结果给出了该环上长为N的(1+uλ)-常循环自对偶码存在的充分条件,得到了该环上长为N的一些常循环自对偶码,并给出了其生成多项式.     

On the weight hierarchy of Preparata codes over Z4

Hammons et al. (see ibid., vol.40, p.301-19, 1994) showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z₄, the so called Preparata code over Z₄. We consider the rth generalized Hamming weight d_r(m) of the Preparata code of length 2^m over Z₄. For any m⩾3, d_r(m) is exactly determined for r=0.5, 1, 1.5, 2, 2.5 and 3.0. For a composite m, we give an upper bound on d_r(m) using the lifting technique. For m=3, 4, 5, 6 and 8, the weight hierarchy is completely determined. In the case of m=7, the weight hierarchy is completely determined except for d₄(7)