q—形变非谐振子广义偶奇相干态及非经典特性

结构了q形变的非谐振子广义偶奇相干态,并运用数值计算方法研究了其非经典特性,结果表明;随q-形变增大,广义偶q－相干态的压缩特性增强而广义奇q－相干态的压缩特性减弱;广义偶q0－相干态的反聚束现象及广义奇q-相干态的聚束现象都减弱。我     

Resilient functions over finite fields

Resilient functions play an important role in the art of information security. In this correspondence, we discuss the existence, construction, and enumeration of resilient functions over finite fields. We show that, for each finite field GF(q) with q > 3, we can easily construct a large number of (q, n, 1, n - 1) resilient functions, most of which include mixing terms. We give a general structure for (q, m + 1, m, 1) resilient functions, and present an example which is not of this general structure. We prove that (q, m + 2, m, 2) resilient functions exist for any m such that 1 < m < q when q > 2. We prove that (q, m + t, m, t) resilient functions exist for any (m, t) such that 1 < m < q and 2 < t < q when q > 3. By making some simple generalizations of former results, we also provide some new methods for constructing resilient functions.     

Explicit construction of families of LDPC codes with no 4-cycles

Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.     

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.     

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.     

有限维Hilbert空间偶q-相干态非经典特性的数值研究

运用数值计算方法研究了ｑ－畸变对有限维Ｈｉｌｂｅｒｔ空间谐振子偶相干态非经典特性的影响．研究表明，随ｑ－畸变增大，偶ｑ－相干态压缩效应减弱，而反聚束效应加强．但其压缩特性在Ｓ＝１的三维空间下与ｑ－畸变无关；而反聚束效应则在ｓ较小的有限维空间无畸变偶相干态下也可出现．     

双模场中Susskind-Glogower相算符的对偶本征矢

找到了双模场中Susskind-Glogower相算符eiφ态矢|(S),q〉的对偶本征矢|(S),q〉*,运用围道积分证明了|(S),q〉*是e-iφ和光子数差算符的共同本征矢.研究了|(S),q〉*的性质,结果是|(S),q〉*及其对偶〈(S),q |构成围道积分形式的完备性,给出了双模场的相态表象.     

非对称两态叠加多模量子叠加态的等幂偶数次方Y压缩

构造了由多模复共轭相干态|{zj(a)*})q和多模虚共轭相干态|{izj(b)*})q两者的线性叠加组成的非对称两态叠加多模量子叠加态|{ψ)q.利用多模压缩态理论,研究了该态的等幂偶数次方Y压缩效应,结果表明:压缩次数N为偶数,即N=2p(p=1,2,3……),并且各个模的初始相位ψf、态|{zj(a)*})q和态|{izj(b)*})q的初始相位差θpq(R)-θnq(I)及其中等序号的各个模的振幅之积Rj(a)Rj(b)的和∑j=1 q [Rj(a)Rj(b)]组成的混合相位θpq(R)-θnq(I)-∑j=1 q [Rj(a)Rj(b)]分别满足一定的条件时,不论p为奇数还是偶数,态|ψ)q的两个正交相位分量交替呈现出周期性变化的等幂偶数次Y压缩效应,p为奇数时的压缩深度大于p为偶数时的压缩深度,这一结果是对称两态叠加多模叠加态所不具有的.     

On the complexity of decoding Reed-Solomon codes (Corresp.)

Certainq-ary Reed-Solomon codes can be decoded by an algorithm requiring onlyO(q log^{2} q)additions and multiplications inGF(q).     

Near-optimal depth-constrained codes

This note considers an n-letter alphabet in which the ith letter is accessed with probability p/sub i/. The problem is to design efficient algorithms for constructing near-optimal, depth-constrained Huffman and alphabetic codes. We recast the problem as one of determining a probability vector q/sup */=(q/sup *//sub 1/,...,q/sup *//sub n/) in an appropriate convex set, S, so as to minimize the relative entropy D(p/spl par/q) over all q/spl isin/S. Methods from convex optimization give an explicit solution for q/sup */ in terms of p. We show that the Huffman and alphabetic codes so constructed are within 1 and 2 bits of the corresponding optimal depth-constrained codes.     

Synthesis and uniqueness of m-sequences over GF(qn) asn-phase sequences over GF(q)

The construction of m-sequences over GF(qⁿ) from known m-sequences over GF(q) is discussed. An algorithm is given which generates m-sequences over GF(qⁿ) from m-sequences over GF(q), where n phase shifts of known m-sequences over GF(q) are determined by the iterative polynomials. It is shown that n shift distinct m-sequences over GF(qⁿ) generated by the same m-sequences over GF(q) are unique when the elements of GF(qⁿ) are represented by n-tuples of the elements from GF(q)     

（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。     

Finite-state trellis representation of CPM

In most of the literature it is claimed that the number of phase states in CPM is equal to q if p is even, and 2q if p is odd, where the modulation index h=p/q. It is shown that a simple assumption due to Fornery (1973) leads to a simplified finite-state representation and also that CPM has q phase states.<>     

Systematic synthesis of combinational circuits using multiplexers

An algorithmic procedure has been developed, suited to computer solution, for a switching function of n variables that can be synthesised by one multiplexer MUX(p, q), (n?q > l) without the necessity of referring to all the possible Ashenhurst's decomposition charts DCn(?q|?n?q).     

On the Stopping Distance of Array Code Parity-Check Matrices

For q an odd prime and 1 les m les q, we study two binary qm times q² parity check matrices for binary array codes. For both parity check matrices, we determine the stopping distance and the minimum distance of the associated code for 2 les m les 3, and for (m, q)=(4, 5). In the case (m, q)=(4, 7), the stopping distance and the related minimum distance are also determined for one of the given parity check matrices. Moreover, we give a lower bound on the stopping distances for m > 3 and q > 3.     

A characterization of MMD codes

Let C be a linear [n,k,d]-code over GF(q) with k⩾2. If s=n-k+1-d denotes the defect of C, then by the Griesmer bound, d⩽(s+1)q. Now, for obvious reasons, we are interested in codes of given defect s for which the minimum distance is maximal, i.e., d=(s+1)q. We classify up to formal equivalence all such linear codes over GF(q). Remember that two codes over GF(q) are formally equivalent if they have the same weight distribution. It turns out that for k⩾3 such codes exist only in dimension 3 and 4 with the ternary extended Golay code, the ternary dual Golay code, and the binary even-weight code as exceptions. In dimension 4 they are related to ovoids in PG(3,q) except the binary extended Hamming code, and in dimension 3 to maximal arcs in PG(2,q)     

Direct calculation by analogue computer of sensitivity coefficients of linear and nonlinear systems

This letter gives a method which enables a direct analysis of sensitivity to parameter variations of linear or nonlinear systems to be simulated on an analogue computer. Based on the automatic changes ± ?q of a parameter q around a value q0, this method enables the dynamic sensitivity coefficient u(t, q0) to be computed with respect to this parameter by comparison of the disturbed solutions obtained in such a way.     

GF(p)上q元旋转对称弹性函数的一个等价刻画

基于旋转对称弹性函数l值支撑矩阵的性质,给出了GF(p)上q变元旋转对称弹性函数的一个等价刻画,证明了GF(p)上q变元旋转对称一阶弹性函数的构造问题等价于一个方程组的求解问题,并且利用方程组的所有解给出这类函数计数结果的一个表示。     

Mode Propagation in a Nonuniform Cylindrical Medium (Correspondence)

A simplified form of the coupling coefficient C(/spl beta//sub p/, /spl beta//sub q/) resulting from a coupled mode theory analysis of wave propagation in a nonuniform medium is derived. It is found for most situations of interest that C(/spl beta//sub p/, /spl beta//sub q/) is proportional to 1/(/spl beta//sub p/-/spl beta//sub q/) and the power transfer between two modes is proportional to 1/(/spl beta//sub p/ - /spl beta//sub q/)/sup 4/. /spl beta//sub p/ and /spl beta//sub q/ are the two different modal propagation constants. For a dielectric rod C(/spl beta//sub p/, /spl beta//sub q/) is a simple line integral around the rod boundary. Approximate forms are presented for optical waveguides.     

A lattice-based systematic recursive construction of quasi-cyclic LDPC codes

This paper presents a low-complexity recursive and systematic method to construct good well-structured low-density parity-check (LDPC) codes. The method is based on a recursive application of a partial Kronecker product operation on a given gamma x q, q ges 3 a prime, integer lattice L(gamma x q). The (n - 1)- fold product of L(gamma x q) by itself, denoted Lⁿ(gamma x q), represents a regular quasi-cyclic (QC) LDPC code, denoted (see PDF), of high rate and girth 6. The minimum distance of (see PDF) is equal to that of the core code (see PDF) introduced by L(gamma x q). The support of the minimum weight codewords in (see PDF) are characterized by the support of the same type of codewords in (see PDF). From performance perspective the constructed codes compete with the pseudorandom LDPC codes.