Codes Of Dimension Research Articles

Singularities of symmetric hypersurfaces and Reed-Solomon codes

We determine conditions on $q$ for the nonexistence of deep holes ofthe standard Reed-Solomon code of dimension $k$ over $\mathbb F_q$generated by polynomials of degree $k+d$. Our conditions rely on theexistence of $q$-rational points with nonzero, pairwise-distinctcoordinates of a certain family of hypersurfaces defined over $\mathbb F_q$.We show that the hypersurfaces under consideration are invariantunder the action of the symmetric group of permutations of thecoordinates. This allows us to obtain critical informationconcerning the singular locus of these hypersurfaces, from which theexistence of $q$-rational points is established.

3-Time-Slot Group-Decodable STBC with Full Rate and Full Diversity

In this paper, we propose a generic method to construct group-decodable space-time block codes (STBC) with arbitrary code dimensions, including odd time slot. Based on the proposed code construction method, 3-time-slot STBC for two transmit antennas with full or even higher code rate can be obtained. The full-rate 3-time-slot STBC obtained can achieve full diversity and symbol-wise decoding complexity. It serves as a solution to the orphan-symbol (3-time-slot) transmit diversity issue raised in 3rd Generation Partnership Project (3GPP) standards.

A Hamada type characterization of the classical geometric designs

The dimension of a combinatorial design $${{\mathcal D}}$$ over a finite field F = GF(q) was defined in (Tonchev, Des Codes Cryptogr 17:121---128, 1999) as the minimum dimension of a linear code over F that contains the blocks of $${{\mathcal D}}$$ as supports of nonzero codewords. There it was proved that, for any prime power q and any integer n � 2, the dimension over F of a design $${{\mathcal D}}$$ that has the same parameters as the complement of a classical point-hyperplane design PG n-1(n, q) or AG n-1(n, q) is greater than or equal to n + 1, with equality if and only if $${{\mathcal D}}$$ is isomorphic to the complement of the classical design. It is the aim of the present paper to generalize this Hamada type characterization of the classical point-hyperplane designs in terms of associated codes over F = GF(q) to a characterization of all classical geometric designs PG d (n, q), where 1 � d � n � 1, in terms of associated codes defined over some extension field E = GF(q t ) of F. In the affine case, we conjecture an analogous result and reduce this to a purely geometric conjecture concerning the embedding of simple designs with the parameters of AG d (n, q) into PG(n, q). We settle this problem in the affirmative and thus obtain a Hamada type characterization of AG d (n, q) for d = 1 and for d > (n � 2)/2.

Insights into the development of face recognition mechanisms revealed by face aftereffects

An important question in person perception is how we acquire the perceptual/cognitive mechanisms that characterize adult expertise. Children's performance on face recognition tests improves dramatically between age 4 and adolescence suggesting that our face recognition system may change during childhood. Yet, the source of this improvement is controversial. In this review, we consider whether changes in the way identity is represented/coded in face space could contribute to this age-related improvement. Face aftereffects have been extensively applied to studying face coding in adults and more recently they have been applied to studying the mechanisms of face coding in children. Face aftereffects are temporary distortions of perception induced by exposure to faces and are thought to reflect the mechanisms underlying face perception. Face aftereffect techniques have revealed that children as young as 4 years of age show evidence of adult-like face space organization, with opponent coding of face dimensions. These findings are consistent with an emerging picture that the key mechanisms of face perception are present early in childhood.

Fractal Analysis on Microstructure Characteristics of Concrete Materials

The fractal characteristics of concrete materials microstructure are analyzed with fractal theory. The fractal dimension of concrete materials microstructure in the different conditions are tested and counted by code and box Dimension. The result shows that the fractal characteristics of concrete materials microstructures are highly notable, as interface of cement clinker mineral, dispersed state of unhydrated cement particles, crack of hardened cement paste, hydration product and pore structure of hydrated cement paste section. Proving it is effective to measure surface of cement clinker mineral, figures of hydration C-S-H grains and outlines, pore structure of concrete section. Using box dimension is effective to test microcracks and pore structure of section of motor samples and fiber-hydrate. In the course of fractal analysis, the dimensions of fractal are bigger than their topologic dimension, and they are smaller than their space dimension, they are keeping with the fractal theory.

On binary codes from conics in [formula omitted

Let A be the q ( q − 1 ) 2 × q ( q − 1 ) 2 incidence matrix of passant lines and internal points with respect to a conic in PG ( 2 , q ) , where q is an odd prime power. In this article, we study both geometric and algebraic properties of the column F 2 -null space L of A . In particular, using methods from both finite geometry and modular presentation theory, we manage to compute the dimension of L , which provides a proof for the conjecture on the dimension of the binary code generated by L .

On the dimension of an APN code

A map f?:?V:?=?GF(2 m ) ? V is APN (almost perfect nonlinear) if its directional derivatives in nonzero directions are all 2-to-1. If m is greater than 2 and f vanishes at 0, then this derivative condition is equivalent to the condition that the binary linear code of length 2 m ???1, whose parity check matrix has jth column equal to ${\omega^j \brack f(\omega^j)}$ , is double-error-correcting, where ? is primitive in V. Carlet et al. (Designs Codes Cryptogr 15:125---156, 1998) proved that this code has dimension 2 m ???1???2m; but their indirect proof uses a subtle argument involving general code parameter bounds to show that a double-error correcting code of this length could not be larger. We show here that this result follows immediately from a well-known result on bent functions ...a subject dear to the heart of Jacques Wolfmann.

Determination on a class of weight hierarchies of <italic>q</italic>-ary linear codes of dimension 5

To determine all possible weight hierarchies of general linear codes is a basic theory having important scientific significance raised in the communication system. But when k or q is larger, it is impossible for q-ary linear codes of dimension k. Reasonable formulation of the problem is modified: to determine almost all the weight hierarchies of q-ary general linear codes of dimension k. Based on the finite projective geometry method, q-ary linear codes of dimension 5 in class V are studied in this paper, in which we find new necessary conditions of weight hierarchies of 5-dimensional codes in class V, and classify the weight hierarchies of 5-dimensional codes in class V into two subclass,and advance subspace set method, and determine almost all the weight hierarchies of q-ary linear codes of dimension 5 in class V. It open the way for the remaining three class of weight hierarchies of 5-dimensional codes, and break through the difficulty. Furthermore, new necessary conditions show that original necessary conditions of weight hierarchies are not enough. We need to develop further new necessary conditions, in order to attack and solve problems of dimension k.

Large constant dimension codes and lexicodes

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\mathbb F$qn with a given dimension. A computer search for large constant dimension codes is usually inefficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient. In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.

THE CLASSIFICATION AND DETERMINATION ON WEIGHT HIERARCHIES OF q-ARY LINEAR CODES OF DIMENSION 5

In This paper,q-ary linear codes of dimension 5 are classified into six classes, and then by using the finite projective geometry method,the weight hierarchies of all linear codes in ClassⅡare determined.

Hybrid encoding method by assembling the magic-matrix scrambling method and the binary encoding method in image hiding

The magic-matrix scrambling method and the binary encoding method are combined to form a hybrid encoding method for hiding digital covert images. For this hybrid encoding method, a covert image is encoded into a host image to form an overt image. First, the magic-matrix scrambling method is used to rearrange all the pixels of the covert image by using a specified magic matrix modified from a magic square to form a scrambled matrix. Then, all the pixels of the scrambled matrix are denoted by binary data. Finally, the binary data are encoded into the host image to form the overt image. The pixels of the overt image contain nine groups of codes used for decoding the covert image, i.e. identification codes, covert-image dimension codes, scrambling-time codes, magic-square dimension codes, corner codes, shifting codes, arrangement codes, graylevel codes, and information codes. The overt image and the host image look almost the same for eyes. Furthermore, the covert image can be decoded directly from the overt image without using the host image. The most important feature is that the decoded covert image is identical to the original covert image, i.e. there is no distortion in the decoding work.

Solving the upside-down puzzle: Why do upright and inverted face aftereffects look alike?

Face aftereffects for upright faces have been widely assumed to derive from face space and to provide useful information about its properties. Yet remarkably similar aftereffects have consistently been reported for inverted faces, a problematic finding because other paradigms argue that inverted faces are processed by different mechanisms from upright faces. Here, we identify a qualitative difference between upright and inverted face aftereffects. Using eye-height aftereffects, we tested for opponent versus multichannel coding of face dimensions by manipulating distance of the adaptor from the average, and face-specific versus shape-generic contributions via transfer of aftereffects between faces and simple T-shapes. Our results argue that (i) inverted face aftereffects derive entirely from shape-generic mechanisms, (ii) upright face aftereffects derive partly from shape-generic mechanisms but also have a substantial face space component, and (iii) both face-specific and shape-generic multidimensional spaces use opponent coding.

Appraisals of Spouse Affiliation and Control during Marital Conflict: Common and Specific Cognitive Correlates Among Facets of Negative Affectivity

The present study examined associations between individual differences in trait negative affect and appraisal biases during a marital conflict discussion in a sample of 300 middle-aged and older couples. We used the interpersonal circumplex (IPC) to quantify specific appraisal biases, defined as discrepancies between participant ratings of their spouses’ levels of hostility, friendliness, and control during a marital disagreement relative to independent behavioral coding of these behavioral dimensions. Further, we examined the specific component affective traits (i.e., anxiety, depression, and anger) individually, as well as their independent effects in simultaneous analyses. Composite negative affectivity was associated with appraisals of the spouse as displaying more control, less friendliness, and more hostility than was evident in independent ratings. For the specific negative affects, depressive tendencies—and perhaps the closely related trait of anxiety—were associated with viewing the spouse as both more hostile and less warm or friendly than did independent observers. In contrast, individuals prone to anger perceived more control in their spouse’s behavior than was rated by observers. The results support interpersonal and cognitive models of the role of appraisals in general negative affectivity and its specific components.

The weight hierarchies of [formula omitted]-ary linear codes of dimension 4

The weight hierarchy of a linear [ n , k ; q ] code C over G F ( q ) is the sequence ( d 1 , d 2 , … , d k ), where d r is the smallest support weight of an r -dimensional subcode of C . In this paper, by using the finite projective geometry method, we determine almost all weight hierarchies of q -ary general linear codes of dimension 4.

Issues on beam-plasma instability: early simulations focusing on the development of a compact neutron generator

The first issue on compact neutron generator design is the definition of the plasma generation process following the analysis of the physical plasma state. The plasma features and the nuclear reactions of fusion involved in the operation of the generator, deuterium-deuterium or deuterium-tritium, as well as the system which determines the trajectories of the particles and the target, are decisive to predict the neutron yield from the generator. Hence, the plasma behavior analysis under established conditions becomes an important evidence. This analysis may be done by means of plasma simulation models. Particle simulation of plasmas, employed since 1960s, provides a picture of the general plasma characteristics. Plasma physics is determined in most cases by simple equations, i.e. equations of motion of electrons, ions and neutrals atoms including the effect of collisions and self-consistent electric and magnetic fields. Computer simulation of plasmas comprises two general areas based on kinetic and fluid. While fluids simulation proceeds by solving numerically the magnetohydrodynamic (MHD) equations, assuming approximate transport coefficients, kinetic simulation considers more detailed models of plasma involving particle interactions through the electromagnetic fields. This article is focused on the simulation and analysis of injected beam into a steady state and periodic plasma. The applied calculation model, for this simulation purpose, is referring to an electrostatic one dimension code, based on kinetic simulation, which simulates periodic plasmas illustrating various fundamental considerations of plasma simulation and make it useful in simulations of the beam optic system for neutron generators. The main goal of this research is explore the PIC code reviewing the computational and physics theory necessary to build the structure of the elementary principles intending to introduce concepts of plasma physics and the computational theory. Moreover, foundations of plasma analysis for neutron generators will be stated

A study of forward error correction for mobile multicast

Abstract3rd Generation Partnership Project (3GPP) has standardized the use of forward error correction (FEC) for the provision of reliable data transmission in the mobile multicast framework. This error control method inevitably adds a constant overhead in the transmitted data. However, it is so simple as to meet a prime objective for mobile multicast services; that is scalability to applications with thousands of receivers. In this paper, we present a study on the impact of application layer FEC on mobile multicast transmissions. We examine whether it is beneficial or not, how the optimal code dimension varies based on network conditions, which parameters affect the optimal code selection, and how this can be done. Additionally, we focus on one of the most critical aspects in mobile multicast transmission, which is power control. The evaluation is performed with the aid of a novel scheme that incorporates the properties of an evolved mobile network, as they are specified by the 3GPP. Copyright © 2010 John Wiley & Sons, Ltd.

Algebraic geometric codes on anticanonical surfaces

Algebraic geometric codes (or AG codes) provide a way to correct errors that occur during the transmission of digital information. AG codes on curves have been studied extensively, but much less work has been done for AG codes on higher dimensional varieties. In particular, we seek good bounds for the minimum distance. We study AG codes on anticanonical surfaces coming from blow-ups of P 2 at points on a line and points on the union of two lines. We can compute the dimension of such codes exactly due to known results. For certain families of these codes, we prove an exact result on the minimum distance. For other families, we obtain lower bounds on the minimum distance.

Reduced-Memory Decoding of Low-Density Lattice Codes

This letter describes a belief-propagation decoder for low-density lattice codes of finite dimension, in which the messages are represented as single Gaussian functions. Compared to previously-proposed decoders, memory is reduced because each message consists of only two values, the mean and variance. Complexity is also reduced because the check node operations are on single Gaussians, avoiding approximations needed previously, and because the variable node performs approximations on a smaller number of Gaussians. For lattice dimension n = 1000 and 10,000, this decoder looses no more than 0.1 dB in SNR, compared to the decoders which use much more memory.

An equivalence of Ward’s bound and its application

It is well known that the MacWilliams transform of the weight enumerator of some code having integer coefficients is equivalent to a set of congruences having integer solutions. In this paper, we prove an equivalent condition of Ward's bound on dimension of divisible codes, which is part of this set of congruences having integer solutions. This new interpretation makes the generalization of Ward's bound an explicit one.

Performance of asynchronous fiber-optic code division multiple access system based on three-dimensional wavelength/time/space codes and its link analysis

A novel family of three-dimensional (3-D) wavelength/time/space codes for asynchronous optical code-division-multiple-access (CDMA) systems with "zero" off-peak autocorrelation and "unity" cross correlation is reported. Antipodal signaling and differential detection is employed in the system. A maximum of [(W x T+1) x W] codes are generated for unity cross correlation, where W and T are the number of wavelengths and time chips used in the code and are prime. The conditions for violation of the cross-correlation constraint are discussed. The expressions for number of generated codes are determined for various code dimensions. It is found that the maximum number of codes are generated for S < or = min(W,T), where W and T are prime and S is the number of space channels. The performance of these codes is compared to the earlier reported two-dimensional (2-D)/3-D codes for asynchronous systems. The codes have a code-set-size to code-size ratio greater than W/S. For instance, with a code size of 2065 (59 x 7 x 5), a total of 12,213 users can be supported, and 130 simultaneous users at a bit-error rate (BER) of 10(-9). An arrayed-waveguide-grating-based reconfigurable encoder/decoder design for 2-D implementation for the 3-D codes is presented so that the need for multiple star couplers and fiber ribbons is eliminated. The hardware requirements of the coders used for various modulation/detection schemes are given. The effect of insertion loss in the coders is shown to be significantly reduced with loss compensation by using an amplifier after encoding. An optical CDMA system for four users is simulated and the results presented show the improvement in performance with the use of loss compensation.