环F4+uF4上线性码及其对偶码的Gray象

研究了环F4+uF4与域F4上的线性码,利用环F4+uF4上码C的Gray重量wG,Gray距离d G和(F4+uF4)n到F4 2n的Gray映射φ,证明了环F4+uF4上线性码C及其对偶码的Gray像φ(C)为F4上的线性码和对偶且dH G(φ(C))dG(C)。同时,给出了F4+uF4上循环码C的Gray像φ(C)为F4上的2-拟循环码。     

Optimal double circulant self-dual codes over F4

Optimal double circulant self-dual codes over F₄ have been found for each length n⩽40. For lengths n⩽14, 20, 22, 24, 28, and 30, these codes are optimal self-dual codes. For length 26, the code attains the highest known minimum weight. For n⩾32, the codes presented provide the highest known minimum weights. The [36,18,12] self-dual code improves the lower bound on the highest minimum weight for a [36,18] linear code     

环F2+uF2的Galois扩张上的迹码

环E＋uF2是介于环Z4与域F4之间的一种四元素环，因此分享了环Z4与域F4的一些好的性质，此环上的编码理论研究成为一个新的热点。该文给出了环E＋uF2的Galois扩张的相关理论，指出此Galois扩环的自同构群不同于Z4环上的Galois扩环的自同构群；定义了Galois扩环上的迹码的概念及子环子码的概念，证明了此Galois扩环上的一个码的对偶码的迹码是该环的子环子码的对偶码。     

Z4×(F2+uF2)上的一类循环码

定义了Z₄×（F₂+uF₂）上的循环码,明确了一类循环码的生成元结构,给出了该类循环码的极小生成元集.利用Gray映射,构造了一些二元非线性码.     

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.     

环F2+uF2上线性码的结构特性

该文研究了环F2 uF2上线性码的结构特性,讨论了环F2 uF2上线性码及其剩余码、挠码和商码之间的关系,通过这些关系.给出了线性码(特别是循环码)的深度分布与深度谱.     

环F2+uF2上线性码及其对偶码的二元象

利用环F2＋uF2上线性码C的生成矩阵给出了码C的对偶码C^┴及其Gray象Ф（C）的生成矩阵，证明了环F2＋uF2上线性码及其对偶码的Gray象仍是对偶码。并由此给出了一个环F2＋uF2如上线性码为自对偶码的充要条件。     

On Type II codes over F4

Previously, Type II codes over F₄ have been introduced as Euclidean self-dual codes with the property that all Lee weights are divisible by four. In this paper, a number of properties of Type II codes are presented. We construct several extremal Type II codes and a number of extremal Type I codes. It is also shown that there are seven Type II codes of length 12, up to permutation equivalence     

环F2+uF2+…+uk-1F2上长为2S的(1+u)-常循环码的距离分布

研究码字的距离分布是编码理论的一个重要研究方向。该文定义了环R=F₂+uF₂+…+u^k-1F₂上的Homogeneous重量,研究了环R上长为2^S的(1+u)-常循环码的Hamming距离和Homogeneous距离。使用了有限环和域的理论,给出了环R上长为2^S的(1+u)-常循环码和循环自对偶码的结构和码字个数。并利用该常循环码的结构,确定了环R上长为2^S的(1+u)-常循环码的Hamming距离和Homogeneous距离分布。     

氟化锂晶体F2心光致电离及F2和F2+心激光特性研究

室温下利用337nm脉冲激光照射着色LiF晶体,有效地将F2心转变成F2+心,其浓度高于1016cm-3。利用消象散三镜折叠腔,研究了LiF晶体F2和F2+心激光特性。实际工作表明,利用氮分子激光作为处理光束,可获得较长时间稳定的F2+心激光输出。     

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     

F2+uF2+…+ukF2环上的循环码

在有限环F2＋uF2＋…＋u^k F2与F2之间定义一个新的Gray映射，证明了该映射是距离保持映射。考察了F2＋uF2＋…＋u^k F2环上循环码，得到了F2＋uF2＋…＋u^k F2环上循环码的生成多项式。最后，证明了F2＋uF2＋…＋u^k F2环上循环码在新定义的Gray映射下的像是F2上的准循环码。     

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     

F_2/H_2链反应脉冲化学激光器简化模型计算

列出了补偿Kerber简化模型缺陷的光引发F_2/H_2链反应脉冲激光器的简化模型。解决了振转跃迁光通量方程与动力学速率方程之间时间坐标的相容性问题。采用Gear自动积分法获得满意的数值计算结果。列出F_2/H_2预反应生成的HF(O)、混合物中O_2含量、光引发剂等对激光性能影响的定量结果。     

Quasi-cyclic codes over Z4 and some new binarycodes

Previously, (linear) codes over Z₄ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z ₄-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z₄ produces a new binary code, a (92, 2²⁴, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials     

Binary images of cyclic codes over Z4

We determine all linear cyclic codes over Z₄ of odd length whose Gray images are linear codes (or, equivalently, whose Nechaev-Gray (1989) image are linear cyclic codes or are linear cyclic codes)     

MDR codes over Zk

In this correspondence, we study maximum distance with respect to rank (MDR) codes over the ring Z_k. We generalize the construction of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon codes and apply the generalized Chinese remainder theorem to construct codes     

光引发F_2/H_2链反应诱导期间的激光现象

紫外动态吸收光谱测定和脉冲HF化学激光简化模型的数值计算结果,确认了反应诱导期的存在。模型计算还表明,在现实的引发水平上(n_F=10~(16)～10~(17)厘米~(-3)),当F_2/H_2,混合物温度降至100K以下时,反应的转化率只有0.3％,而激光输出能量大大降低。A.CBamRn~等关于F_2/H_2链反应脉冲激光器在100K工作的设想似难可取。     

LiF晶体F_2色心可调谐激光器

本文报导以0.53微米激光作为泵浦的LiF:F_2色心可调谐激光器。实验所用的晶体的F_2心浓度约为6.2×10~(17)厘米~(-3),高于已有报导值。0.69微米附近可调谐激光输出线宽为1.5埃,能量转换效率为2.9％。晶体在连续运转6千个脉冲后,才开始出现漂白效应。     

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)