Dual-observer design procedure

A procedure is described for the design of a dual observer of order (q?1), for a linear system of order n, where q is the controllability index. All (n+q?1) poles of the composite system may be assigned arbitrary values.     

Simple method for computing elements of order 2kn, where n|2p?1?1 and 2 ? k ? p+1, in GF[(2p?1)2]

A simple method is developed for computing elements of order 2kn, where n|2p?1?1 and 2 ? k ? p+1, in the Galois field GF(q2), and q = 2p?1 is a Mersenne prime. Such primitive elements are needed to implement complex number-theoretic transforms.     

Real-frequency interpolation with positive-real n ports

A procedure is described for generating passive lumped nports that interpolate to prescribed n×n `passive? matrices at designated points on the real-frequency j? axis. In those cases where the given matrices are `lossless?, the resulting n ports can be constructed with no more than 2qn reactive elements (q is the number of frequencies), whereas, in the general case, 4qn elements are used.     

Combinational logicfree realisations for high-speed m-sequence generation

A combinational logicfree F.S.R. construction is specified which allows the high speed generation of m-sequences. These constructions are based on characteristic polynomials of the form (1 ? x)q ? xp and they can be designed so as to produce sequences based on primitive trinomial recurrences of the form xn = xn?q ? xn?p at a rate q times as fast as the basic shift pulse rate.     

Improving the Gilbert-Varshamov bound for q-ary codes

Given positive integers q,n, and d, denote by A/sub q/(n,d) the maximum size of a q-ary code of length n and minimum distance d. The famous Gilbert-Varshamov bound asserts that A/sub q/(n,d+1)/spl ges/q/sup n//V/sub q/(n,d) where V/sub q/(n,d)=/spl Sigma//sub i=0//sup d/ (/sub i//sup n/)(q-1)/sup i/ is the volume of a q-ary sphere of radius d. Extending a recent work of Jiang and Vardy on binary codes, we show that for any positive constant /spl alpha/ less than (q-1)/q there is a positive constant c such that for d/spl les//spl alpha/n A/sub q/(n,d+1)/spl ges/cq/sup n//V/sub q/(n,d)n. This confirms a conjecture by Jiang and Vardy.     

Approximation Formulas for Reliability with Repair

A system consists of n-identical parallel subsystems, each having an exponential distribution of times to failure and an exponential distribution of times to repair. The system reliability with repair is the probability of no more than q out of n subsystems being simultaneously in a failed state during time t. Under conditions frequently met in practice, system reliability with repair R(t) can be approximated by: R(t) ? exp [?t/Tm] where Tm is the mean time for the system to pass for the first time from zero to (q + 1) simultaneous subsystem failures. Exact and approximate methods of calculating Tm are developed. A detailed error analysis is presented showing the limitations of using Tm to calculate system reliability with repair.     

New class of nonlinear systematic error detecting codes

A code C detects error e with probability 1-Q(e),ifQ(e) is a fraction of codewords y such that y, y+e/spl isin/C. We present a class of optimal nonlinear q-ary systematic (n, q/sup k/)-codes (robust codes) minimizing over all (n, q/sup k/)-codes the maximum of Q(e) for nonzero e. We also show that any linear (n, q/sup k/)-code V with n /spl les/2k can be modified into a nonlinear (n, q/sup k/)-code C/sub v/ with simple encoding and decoding procedures, such that the set E={e|Q(e)=1} of undetected errors for C/sub v/ is a (k-r)-dimensional subspace of V (|E|=q/sup k-r/ instead of q/sup k/ for V). For the remaining q/sup n/-q/sup k-r/ nonzero errors, Q(e)/spl les/q/sup -r/for q/spl ges/3 and Q(e)/spl les/ 2/sup -r+1/ for q=2.     

Zero-loss second-order ring modulator

It is shown that zero conversion loss may be obtained for the frequency change from ?q to 2?p ± ?q using an ideal ring modulator switched at a frequency ?p and having a reactive idler circuit at the normal output terminals. The frequency 2 ?p ± ?q is obtained at the normal input terminals, so that advantages are obtained with regard to earthing arrangements.     

Comment on `Rational approximants to the matrix exponential? [and reply]

The matrix exponential exp(At) may be approximated to in some circumstances by the matrix function ?p,q(At), where ?p,q(u) is a Padé approximant to exp(u). The approximation breaks down if A has large latent roots, and in this case may be replaced by {?p,q(At/r)}r for some integer r. An error analysis of the latter approximation is given. A reply from the original author follows.     

对大整数n=pq分解的一个有效的搜索算法

本文通过构造一个简单的基于调差思想的搜索算法和一个快速的开方算法对满足一定条件的大整数n=pq(p、q为大素数 )进行快速分解 .从而指出基于因子分解的密码体制中存在着相当多的弱密钥 ,而且很难避免选取这些弱密钥 .这对于我们分析基于因子分解的公钥体制的安全性是很有意义的     

List decoding of q-ary Reed-Muller codes

The q-ary Reed-Muller (RM) codes RM/sub q/(u,m) of length n=q/sup m/ are a generalization of Reed-Solomon (RS) codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for RM codes were given in and . The algorithm in Sudan et al. (1999) is an improvement of the algorithm in , it is applicable to codes RM/sub q/(u,m) with u相似文献   

2700V4H-SiC结势垒肖特基二极管

在76.2 mm 4H-SiC晶圆上采用厚外延技术和器件制作工艺研制的结势垒肖特基二极管(JBS).在室温下,器件反向耐压达到2700 V.正向开启电压为0.8V,在VF=2V时正向电流密度122 A/cm2,比导通电阻Ron=8.8 mΩ·cm2.得到肖特基接触势垒qφв=1.24 eV,理想因子n=1.     

Constructions and properties of Costas arrays

A Costas array is an n × n array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots. As a frequency-hop pattern for radar or sonar, a Costas array has an optimum ambiguity function, since any translation of the array parallel to the coordinate axes produces at most one out-of-phase coincidence. We conjecture that n × n Costas arrays exist for every positive integer n. Using various constructions due to L. Welch, A. Lempel, and the authors, Costas arrays are shown to exist when n = p - 1, n = q - 2, n = q - 3, and sometimes when n = q - 4 and n = q - 5, where p is a prime number, and q is any power of a prime number. All known Costas array constructions are listed for 271 values of n up to 360. The first eight gaps in this table occur at n = 32, 33, 43, 48, 49, 53, 54, 63. (The examples for n = 19 and n = 31 were obtained by augmenting Welch's construction.) Let C(n) denote the total number of n × n Costas arrays. Costas calculated C(n) for n ≤ 12. Recently, John Robbins found C(13) = 12828. We exhibit all the arrays for n ≤ 8. From Welch's construction, C(n) ≥ 2n for infinitely many n. Some Costas arrays can be sheared into "honeycomb arrays." All known honeycomb arrays are exhibited, corresponding to n = 1, 3, 7, 9, 15, 21, 27, 45. Ten unsolved problems are listed.     

Calculation of transient response

Given the rational algebraic function X(s) = an?1Sn?1+an?2Sn?2+?+a1s+a0/sn+bn?1sn?1+?+b1s+b0 it is shown that the corresponding time function is expressed simply by the linear combination x(t) = an?1qn?1(t)+an?2qn?2(t) +? +a1q1(t) + a0q0(t) where functions qt(t) are the last column elements of the transition matrix M(t) = exp (At).     

Constructing SCN bases in characteristic 2

A simple deterministic algorithm to construct a normal basis of GF(qⁿ) over GF(q) (q=p^r, p prime) is given. When p=2, the authors deduce a (self complementary normal-SCN) basis of GF(q ⁿ) over GF(q) for n odd, or n=2t, t odd. In characteristic 2 these cases are known to be the only possible ones for which there exists an SCN basis     

On MDS extensions of generalized Reed- Solomon codes

An(n, k, d)linear code overF=GF(q)is said to be {em maximum distance separable} (MDS) ifd = n - k + 1. It is shown that an(n, k, n - k + 1)generalized Reed-Solomon code such that2leq k leq n - lfloor (q - 1)/2 rfloor (k neq 3 {rm if} qis even) can be extended by one digit while preserving the MDS property if and only if the resulting extended code is also a generalized Reed-Solomon code. It follows that a generalized Reed-Solomon code withkin the above range can be {em uniquely} extended to a maximal MDS code of lengthq + 1, and that generalized Reed-Solomon codes of lengthq + 1and dimension2leq k leq lfloor q/2 rfloor + 2 (k neq 3 {rm if} qis even) do not have MDS extensions. Hence, in cases where the(q + 1, k)MDS code is essentially unique,(n, k)MDS codes withn > q + 1do not exist.     

（p＋q）端口回转器及其群特性

本文提出了一类多端口电阻元件－（ｐ＋ｑ）端合回转器，用群论的方法研究了所有（ｐ＋ｑ）端口回转器与变压器构成的集合ＧＩＴ（ｐ＋ｑ）。结果表明，当ｐ＝ｑ＝ｎ时，ＧＩＴ（２ｎ）构民群，同时还讨论了（ｐ＋ｑ）端口回转器的分解，电路实现方法和应用。     

序列k-错线性复杂度算法

本文给出了一个测量流密码序列稳定性的重要指标Ｋ－错线性复杂度的算法,即求ＧＦ（ｑ）上（ｑ＝ｐ＾ｍ,ｐ：素数）周期为Ｎ＝ｐ＾ｎ序列的Ｋ－错线性复杂度的快速算法。在这里对广义ＧａｍｅｓＣｈａｎ算法－ＧＦ（ｑ）上ｐ＾ｎ序列线性复杂度算法进行了简化,并给出了ＧＦ（ｑ）上ｐ＾ｎ序列Ｋ－错线性复杂度算法及其证明。     

Simple MAP decoding of first-order Reed-Muller and Hamming codes

A maximum a posteriori (MAP) probability decoder of a block code minimizes the probability of error for each transmitted symbol separately. The standard way of implementing MAP decoding of a linear code is the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, which is based on a trellis representation of the code. The complexity of the BCJR algorithm for the first-order Reed-Muller (RM-1) codes and Hamming codes is proportional to n/sup 2/, where n is the code's length. In this correspondence, we present new MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes. The proposed algorithms have complexities proportional to q/sup 2/n log/sub q/n, where q is the alphabet size. In particular, for the binary codes this yields complexity of order n log n.     

量子突发纠错乘积码的构造

量子突发纠错码是以CSS量子码的纠错原理和构造技术为基础,在量子计算和量子通信中有着十分重要的作用。首次利用GF(q)上的任意线性码C1=〖JB([〗n,k1,d1q和满足对偶包含关系的BCH码C2=〖JB([〗n,k2,d2q,来构造乘积码C1C2和(C1C2)⊥,当满足n2>2k1k2时,在CSS构造的基础上便可构造参数为[[n2,n2－n]]的量子突发纠错乘积码,并给出其突发纠错能力。