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     

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     

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     

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。     

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     

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)     

Optimal self-dual codes over F/sub 2//spl times/F/sub 2/ with respect to the Hamming weight

In this paper, we study optimal self-dual codes and type IV self-dual codes over the ring F/sub 2//spl times/F/sub 2/ of order 4. We give improved upper bounds on minimum Hamming and Lee weights for such codes. Using the bounds, we determine the highest minimum Hamming and Lee weights for such codes of lengths up to 30. We also construct optimal self-dual codes and type IV self-dual codes.     

Na_2(b~3Σ_g~ )→Na_2(x~3Σ_u~ )发射光谱

用XeF激光的351毫米微来激励Na_2(x~1Σ_g~ )得到c~1Π_u→2~1Σ_g~ 跃迁范围内三条受激发射谱线及b~3Σ_g~ →x~3Σ_u~ 830毫微米至900毫微米准连续发射谱。文中讨论了这两个跃迁的关联并估计了产生激光振荡的可能性。     

Circulant based extremal additive self-dual codes over GF(4)

It is well known that the problem of finding stabilizer quantum-error-correcting codes (QECC) is transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to classify the extremal additive circulant self-dual codes of lengths up to 15, and construct good codes for lengths 16/spl les/n/spl les/27. We also classify the extremal additive 4-circulant self-dual codes of lengths 4,6,8,12,14, and 16 and most codes of length 10, and construct good codes of even lengths up to 22. Furthermore, we classify the extremal additive bordered 4-circulant self-dual codes of lengths 3,5,7,9,11,13,15, and 17, and construct good codes for lengths 19,21,23, and 25. We give the current status of known extremal (or optimal) additive self-dual codes of lengths 12 to 27.     

Cyclic and negacyclic codes over finite chain rings

The structures of cyclic and negacyclic codes of length n and their duals over a finite chain ring R are established when n is not divisible by the characteristic of the residue field R~. Some cases where n is divisible by the characteristic of the residue field R~ are also considered. Namely, the structure of negacyclic codes of length 2/sup t/ over /spl Zopf//sub 2//sup m/ and that of their duals are derived.     

F_2/Ne/Kr混合气体中三原子准分子Kr_2F形成速率常数的测定

本工作用Ne代替Ar作为缓冲气体,在快放电激励条件下,对Kr_2F的动力学过程进行了研究,观察到较强的Kr_2F荧光辐射,并用时间积分谱的方法测定了Kr_2F的三体形成速率常数。本文还指出了用Ne作为缓冲气体比用Ar作为缓冲气体更有利于增强Kr_2F的辐射。     

室温运转的LiF晶体F_2色心激光器的实验研究

以YAG:Nd~(3+)激光器二次谐波0.532微米激光为泵源,对室温条件下运转的重复脉冲工作的LiF晶体F_2心激光器做了初步的实验研究和机理的讨论.     

Z2k-linear codes

We introduce a generalization to Z₂k of the Gray map and generalized versions of Kerdock and Delsarte-Goethals codes     

高效率开关F3/E类功率放大器

介绍了一种高效F3/E类功率放大器的设计方法,该放大器将F类功率放大器的谐波控制电路引入逆E类功率放大器的负载网络,以改善放大器性能。此电路结构提升了放大器的功率输出能力,降低了电路对功率放大器管器件漏极耐压特性的要求,增强了器件工作时的安全性。详细阐述了该放大器的设计过程,并给出了负载网络各器件的最佳设计取值方程。选用GaNHEMT器件研制了S频段F3/E类功率放大器测试电路。实测结果表明该放大器在驱动功率为27 dBm时,可获得40.3 dBm的输出功率,具有13.3 dB增益,工作效率高达78.1%,功率附加效率为75.2%。实测结果与仿真结果吻合,验证了设计方法的正确性。     

Cyclic block codes definable over multiple finite fields

It is shown that there exists a class of error correcting codes which can be viewed both as binary cyclic codes and as multilevel cyclic codes. This class contains not only the Burton codes but also some Reed Solomon codes. The conditions which codes of this class must satisfy are explained and some simple examples are given