On ℤ2ℤ2[u]-additive codes

In this paper, a new class of additive codes which is referred to as ?₂ ?₂[u]-additive codes is introduced. This is a generalization towards another direction of recently introduced ?₂ ?₄-additive codes [J. Borges, C. Fernández-Córdoba, J. Pujol, J. Rif´a, and M. Villanueva, ?₂ ?₄-linear codes: Generator matrices and duality, Designs Codes Cryptogr. 54(2) (2010), pp. 167–179]. ?₂ ?₄-additive codes have shown to provide a promising class of codes with their algebraic structure and applications such as steganography. The standard generator matrices are established and by introducing orthogonality the parity-check matrices are also obtained. A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, a Gray map that maps these codes to binary codes is defined and some examples of optimal codes which are the binary Gray images of ?₂ ?₂[u]-additive codes are presented.     

环F2+uF2+u2F2上的(1+u+u2）—循环码*

通过定义一种从环F2+uF2+u2F2到域F2上新的Gray映射,将环F2+uF2+u2F2上的线性(1+u+u2)—循环码等距映射成域F2的线性循环码;进一步又给出了在码长n=3(mod 4)时环F2+uF2+u2F2上的线性(1+u+u2)—循环码的Gray象的生成多项式,这对构造新的好码具有重要意义。     

Structure of steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m + 2 over \mathbb{F}_2

The structure of all different Steiner triple systems S(2 ^m ?1, 3, 2) of rank 2 ^m ?m+2 over $\mathbb{F}_2 $ is described. This induces a natural recurrent method for constructing Steiner triple systems of any rank. In particular, the method gives all different such systems of order 2 ^m ? 1 and rank ≤ 2 ^m ? m + 2. The number of such different systems of order 2 ^m ? 1 and rank less than or equal to 2 ^m ? m + 2 which are orthogonal to a given code is found. It is shown that all different triple Steiner systems of order 2 ^m ? 1 and rank ≤ 2 ^m ? m + 2 are derivative and Hamming. Furthermore, all such triples are embedded in quadruple systems of the same rank and in perfect binary nonlinear codes of the same rank.     

Explicit solutions to the quaternion matrix equations X−AXF=C and X−A[Xtilde] F=C

In the present paper, we investigate the quaternion matrix equation X?AXF=C and X?A[Xtilde] F=C. For convenience, we named the quaternion matrix equations X?AXF=C and X?A[Xtilde] F=C as quaternion Stein matrix equation and quaternion Stein-conjugate matrix equation. Based on the Kronecker map and complex representation of a quaternion matrix, we give the solution expressions of the quaternion Stein matrix equation and quaternion Stein-conjugate matrix equation. Through these expressions, we can easily obtain the solution of the above two equations. In order to compare the direct algorithm with the indirect algorithm, we propose an example to illustrate the effectiveness of the proposed method.     

环F2+uF2上长为2e的重根循环码与(1+u)-循环码的秩

通过对环F2 uF2上长为2e的重根循环码与(1 u)-循环码结构的讨论,具体给出了它们的秩和极小生成元集.这对确定码的距离分布以及译码均有重要的意义.     

Efficient approaches for ℓ2-ℓ0 regularization and applications to feature selection in SVM

For solving a class of ?₂- ?₀- regularized problems we convexify the nonconvex ?₂- ?₀ term with the help of its biconjugate function. The resulting convex program is explicitly given which possesses a very simple structure and can be handled by convex optimization tools and standard softwares. Furthermore, to exploit simultaneously the advantage of convex and nonconvex approximation approaches, we propose a two phases algorithm in which the convex relaxation is used for the first phase and in the second phase an efficient DCA (Difference of Convex functions Algorithm) based algorithm is performed from the solution given by Phase 1. Applications in the context of feature selection in support vector machine learning are presented with experiments on several synthetic and real-world datasets. Comparative numerical results with standard algorithms show the efficiency the potential of the proposed approaches.     

环[F2+uF2+vF2]上的[(1+v)-]常循环码

研究了环[R=F2+uF2+vF2] 上的[(1+v)-]常循环码。利用环[R]上奇长循环码的生成元来刻画环[R]上奇长的[(1+v)-]常循环码,进而给出了[Rn]到[(F2+uF2)2n]的一个广义Gray映射[φ],证明了环[R]上的[(1+v)-]常循环码[C]在[φ]下的广义Gray像[φ(C)]是环[F2+uF2]上的循环码。     

Steiner triple systems S(2 m ? 1, 3, 2) of rank 2 m ? m+ 1 over \mathbb{F}_2

Steiner systems S(2 ^m ? 1, 3, 2) of rank 2 ^m ? m+1 over the field $\mathbb{F}_2$ are considered. A new recursive method for constructing Steiner triple systems of an arbitrary rank is proposed. The number of all Steiner systems of rank 2 ^m ? m+1 is obtained. Moreover, it is shown that all Steiner triple systems S(2 ^m ? 1, 3, 2) of rank r ?? 2 ^m ? m+1 are derived, i.e., can be completed to Steiner quadruple systems S(2 ^m , 4, 3). It is also proved that all such Steiner triple systems are Hamming; i.e., any Steiner triple system S(2 ^m ? 1, 3, 2) of rank r ?? 2 ^m ? m + 1 over the field $\mathbb{F}_2$ occurs as the set of words of weight 3 of a binary nonlinear perfect code of length 2 ^m ?1.     

Hyperspectral unmixing employing l1−l2 sparsity and total variation regularization

ABSTRACT

Hyperspectral unmixing is essential for image analysis and quantitative applications. To further improve the accuracy of hyperspectral unmixing, we propose a novel linear hyperspectral unmixing method based on l₁?l₂ sparsity and total variation (TV) regularization. First, the enhanced sparsity based on the l₁?l₂ norm is explored to depict the intrinsic sparse characteristic of the fractional abundances in a sparse regression unmixing model because the l₁?l₂ norm promotes stronger sparsity than the l₁ norm. Then, TV is minimized to enforce the spatial smoothness by considering the spatial correlation between neighbouring pixels. Finally, the extended alternating direction method of multipliers (ADMM) is utilized to solve the proposed model. Experimental results on simulated and real hyperspectral datasets show that the proposed method outperforms several state-of-the-art unmixing methods.     

An efficient RNS parity checker for moduli set {2^n-1, 2^n＋1, 2^2n＋1} and its applications

Residue number system （RNS） has received considerable attention since decades before, because it has inherent carry-free and parallel properties in addition, sub- traction, and multiplication operations. For an odd moduli set, the fundamental problems in RNS, such as number comparison, sign determination, and overflow detection, can be solved based on parity checking. The paper proposes a parity checking algorithm along with related propositions and the certification based on the celebrated Chinese remainder theory （CRT） and mixed radix conversion （MRC） for the moduli set {2^n-1, 2^n＋1, 2^2n＋1}. The parity checker consists of two modular adders and a carry-look-ahead chain. The hardware implementation requires less area and path delay. Besides, the implementations of number comparison, sign determination, and overflow detection, which are based on this parity checker, are also performed in this paper. And this kind of parity checker can be used as a basic element to design ALUs and DSP module in RNS.     

高清接收机的最新进展——第2代中大3688M(F1/F2)高清三合一接收机

高清的免费频道,此消彼长。这边刚加密了VOOM-HD和NGC-HD,那头又来了Discovery-HD及124HD。追星族手中的武器,早已升级换代。高清总动员的网友们,人手都有三合一。DVB-S2,H.264,AAC等等,逐渐成了业内流行的词汇。有了三合一,等于买了三保险。没有地面高清吗?那就收有线高清。没有有线高清吗?那就收卫星高清。不管你在什么地方,总能找到高清。买三合一,玩的就是高清。有人说三合一要能共享,他就买,殊不知目前的高清频道大都无法共享。你想看共享的标清频道,那不如买DM500算了,不但便宜,而且看标清的画质还好过三合一。     

Analytical Expansion and Numerical Approximation of the Fermi–Dirac Integrals F j(x) of Order j=−1/2 and j=1/2

This paper uses properties of the Weyl semiintegral and semiderivative, along with Oldham's representation of the Randles–Sevcik function from electrochemistry, to derive infinite series expansions for the Fermi–Dirac integrals _j (x), –j=–1/2, 1/2. The practical use of these expansions for the numerical approximation of _–1/2(x) and _1/2(x) over finite intervals is investigated and an extension of these results to the higher order cases j=3/2, 5/2, 7/2 is outlined.     

Vasil’ev codes of length n = 2m and doubling of Steiner systems S(n, 4, 3) of a given rank

Extended binary perfect nonlinear Vasil’ev codes of length n = 2^m and Steiner systems S(n, 4, 3) of rank n-m over F ₂ are studied. The generalized concatenated construction of Vasil’ev codes induces a variant of the doubling construction for Steiner systems S(n, 4, 3) of an arbitrary rank r over F ₂. We prove that any Steiner system S(n = 2^m, 4, 3) of rank n-m can be obtained by this doubling construction and is formed by codewords of weight 4 of these Vasil’ev codes. The length 16 is studied in detail. Orders of the full automorphism groups of all 12 nonequivalent Vasil’ev codes of length 16 are found. There are exactly 15 nonisomorphic systems S(16, 4, 3) of rank 12 over F ₂, and they can be obtained from codewords of weight 4 of the extended Vasil’ev codes. Orders of the automorphism groups of all these Steiner systems are found.