On the Minimum Weight of Codes over F5 Constructed from Certain Conference Matrices

In this paper, codes over F₅ with parameters [36, 18, 12], [48, 24, 15], [60, 30, 18], [64, 32, 18] and [76, 38, 21] which improve the previously known bounds on the minimum weight for linear codes over F₅ are constructed from conference matrices. Through shortening and truncating, the above codes give numerous new codes over F₅ which improve the previously known bounds on minimum weights.     

Failed disk recovery in double erasure RAID arrays

Reliability is a major concern in the design of large disk arrays. In this paper, we examine the effect of encountering more failures than that for which the RAID array was initially designed. Erasure codes are incorporated to enable system recovery from a specified number of disk erasures, and strive beyond that threshold to recover the system as frequently, and as thoroughly, as is possible. Erasure codes for tolerating two disk failures are examined. For these double erasure codes, we establish a correspondence between system operation and acyclicity of its graph model. For the most compact double erasure code, the full 2-code, this underlies an efficient algorithm for the computation of system operation probability (all disks operating or recoverable).When the system has failed, some disks are nonetheless recoverable. We extend the graph model to determine the probability that d disks have failed, a of which are recoverable by solving one linear equation, b of which are further recoverable by solving systems of linear equations, and d−a−b of which cannot be recovered. These statistics are efficiently calculated for the full 2-code by developing a three variable ordinary generating function whose coefficients give the specified values. Finally, examples are given to illustrate the probability that an individual disk can be recovered, even when the system is in a failed state.     

A T-matrix method and computer code for randomly oriented, axially symmetric coated scatterers

A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input-output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres.     

便携式条形码阅读器的设计

本设计为一种便携式条形码阅读译码器（简称阅读器），它采用ＩＮＴＥＬ８０３１ＣＰＵ微处理器为主芯片，辅以其它大规模集成电路芯片，构成一智能化系统，阅读及识别采用Ｃｏｄｅ３９码编制的条形码，并能完成条形码信息的存储、数目统计及与微机进行串行通信功能。     

Symplectic spread-based generalized Kerdock codes

Kerdock codes (Kerdock, Inform Control 20:182–187, 1972) are a well-known family of non-linear binary codes with good parameters admitting a linear presentation in terms of codes over the ring (see Nechaev, Diskret Mat 1:123–139, 1989; Hammons et al., IEEE Trans Inform Theory 40:301–319, 1994). These codes have been generalized in different directions: in Calderbank et al. (Proc Lond Math Soc 75:436–480, 1997) a symplectic construction of non-linear binary codes with the same parameters of the Kerdock codes has been given. Such codes are not necessarily equivalent. On the other hand, in Kuzmin and Nechaev (Russ Math Surv 49(5), 1994) the authors give a family of non-linear codes over the finite field F of q = 2 ^l elements, all of them admitting a linear presentation over the Galois Ring R of cardinality q ² and characteristic 2². The aim of this article is to merge both approaches, obtaining in this way new families of non-linear codes over F that can be presented as linear codes over the Galois Ring R. The construction uses symplectic spreads.      

Generating 2-Gray codes for ballot sequences in constant amortized time

We present a simple algorithm that generates a cyclic 2-Gray code for ballot sequences. The algorithm generates each ballot sequence in constant amortized time using a linear amount of space. This is the first known cyclic 2-Gray code for ballot sequences that achieves this time bound. In addition, the algorithm can be easily modified to output ballot sequences in binary reflected Gray code order in constant amortized time per string using a linear amount of space.     

陆基无线扩频定位系统中伪随机码设计

讨论了无线扩频定位系统的关键技术之一——扩频码的设计与实现。首先从实验的角度基于Logistic映射，分析了其所生成的混沌序列的部分相关特性及平衡性，给出了计算机仿真结果；最后从工程角度给出了易于实现的平衡Gold码的设计方法。     

Chemical Evolution of a Bacterial Proteome

We have changed the amino acid set of the genetic code of Escherichia coli by evolving cultures capable of growing on the synthetic noncanonical amino acid L ‐β‐(thieno[3,2‐b]pyrrolyl)alanine ([3,2]Tpa) as a sole surrogate for the canonical amino acid L ‐tryptophan (Trp). A long‐term cultivation experiment in defined synthetic media resulted in the evolution of cells capable of surviving Trp→[3,2]Tpa substitutions in their proteomes in response to the 20 899 TGG codons of the E. coli W3110 genome. These evolved bacteria with new‐to‐nature amino acid composition showed robust growth in the complete absence of Trp. Our experimental results illustrate an approach for the evolution of synthetic cells with alternative biochemical building blocks.     

Spontaneous Formation of RNA Strands,Peptidyl RNA,and Cofactors

How the biochemical machinery evolved from simple precursors is an open question. Here we show that ribonucleotides and amino acids condense to peptidyl RNAs in the absence of enzymes under conditions established for genetic copying. Untemplated formation of RNA strands that can encode genetic information, formation of peptidyl chains linked to RNA, and formation of the cofactors NAD⁺, FAD, and ATP all occur under the same conditions. In the peptidyl RNAs, the peptide chains are phosphoramidate‐linked to a ribonucleotide. Peptidyl RNAs with long peptide chains were selected from an initial pool when a lipophilic phase simulating the interior of membranes was offered, and free peptides were released upon acidification. Our results show that key molecules of genetics, catalysis, and metabolism can emerge under the same conditions, without a mineral surface, without an enzyme, and without the need for chemical pre‐activation.