Reversible Codes Research Articles

New necessary conditions for abelian hadamard difference sets

In this paper, we obtain several nonexistence results for abelian Hadamard difference sets. In particular, we prove that there are no Hadamard difference sets in abelian groups G = Z 2 × Z 2 × P, where | P| = p 2 α , α is odd and p is a prime congruent to 1 (mod 4). Also, we give a detailed proof for a connection between certain reversible Hadamard difference sets and projective three-weight codes which was claimed in Xiang and Chen (1996).

A cyclic [6,3,4] group code and the hexacode over GF(4)

A [6,3,4] code E/sub 6/ over an Abelian group A/sub 4/ with four elements is presented. E/sub 6/ is cyclic, unlike the [6,3,4] hexacode H/sub 6/ over GF(4). However, E/sub 6/ and H/sub 6/ are isomorphic when the latter is viewed as a group code. Differences and similarities between E/sub 6/ and H/sub 6/ are discussed. A dual code of E/sub 6/ is presented. Some binary codes, among them the [24,12,8] Golay, are derived with the aid of E/sub 6/. A related cyclic [4,2,3] code E/sub 4/* is applied to construct the Nordstrom-Robinson code. E/sub 6/ is the smallest member of a class of [2k,k,4] cyclic and reversible codes over A/sub 4/. Another class of cyclic and reversible codes of length 2l+1; l/spl ges/2 and minimum distance 3 over A/sub 4/ is also presented.

A Confirmatory Factor Analysis Examination of Reverse Coding Effects in Meyer and Allen's Affective and Continuance Commitment Scales

Examination of Meyer and Allen's Affective and Continuance Commitment Scales using confirmatory factor analysis with LISREL 7 provided strong support across multiple diagnostics for the existence of a reverse coding method factor defined by the six negatively worded items in the scales.

チェーン符号化を用いた自動車用地図画像の可逆符号化方式

カーナビゲーション用のディジタル地図画像を高能率に可逆圧縮する手法を提案する.地図画像を道路部分と背景部分に分離し, 各々に適したチェーン符号化を適用する.交差点の認識や道路の直線性等を利用した種々の工夫を施すことにより, JBIGを上回る高い圧縮率を達成した.

Constructing a better cyclic code than cyclic Reed-Solomon code

Problems of computing the generator polynomial for a (q+1, q-d+2) reversible cyclic BCH code over GF(q), q=p/sup m/, having the minimum Hamming distance d, are presented. The considered code is almost as short as a Reed-Solomon (RS) code but it generates codewords with two information symbols more than the codewords of RS code with the same minimum Hamming distance. >

Reversible variable length codes

Proposes some reversible variable length codes (RVLCs) which can be decoded instantaneously both in the forward and backward directions and have high transmission efficiency. These codes can be used, for example, in the backward reconstruction of video signals from the data last received when some signal is lost midway in the transmission. Schemes for a symmetrical RVLC requiring only a single code table and for an asymmetrical RVLC having short average code length are introduced. They compare favorably with other reversible codes such as B2 codes in several aspects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reversible subband coding of images

AbstractIn conventional 1D filter banks used for reversible subband coding of gray‐level still images, the high‐band signals are extrapolative or interpolative prediction error signals, the former using one side of the pixels alone and the latter using two sides of the pixels but with levels four times that of the input signals.This paper proposes a reversible subband coding method which has a high compression efficiency by reducing the entropy of the high‐band signal. This method employs 1D filter banks which use interpolative prediction error signals having levels twice that of the input signal as the high‐band signals.This paper also describes the design of non‐separable filter banks which predict a pixel in question by using four pixels around the point. The compression efficiency of the proposed method has been compared with the conventional method by using real images. The results show the following: the entropy of the proposed method is smaller than the conventional method by 0.1 to 0.5 bits/pel; some samples processed by the proposed method show a higher compression efficiency than those in the reversible predictive coding; the separable filter banks have a higher compression efficiency than the nonseparable filter banks (both based on the proposed method); and the reduced images using the proposed separable method with a lowpass filter have many taps to suppress aliasing.

Site-directed mutagenesis of HIV reverse transcriptase to probe enzyme processivity and drug binding.

Site-directed mutagenesis has demonstrated that changes within the human immunodeficiency virus reverse transcriptase coding sequence alone can account for viral resistance to inhibitors. Inhibitor sensitivity of mutant enzymes in vitro correlates with the sensitivity of the virus to non-nucleoside inhibitors observed in vivo, but this is not the case with nucleoside analogs. Recent structural, kinetic, and site-directed mutagenesis studies demonstrate the importance of enzyme-nucleic acid contacts in determining enzyme sensitivity to inhibitors in vitro, as well as how accurately the reverse transcriptase synthesizes DNA.

Multicast source routing in packet-switched networks

In this paper we present an address coding mechanism for multicast source routing packets in packet-switched networks. A simple algorithm for processing these address codes at intermediate output link adaptors is presented. It involves only the recognition of a particular link label at the front part of the address code and the stripping off of a front segment of the address code and so can easily be implemented in hardware. Recognizing that the recipients of a multicast packet very often need to respond to the source node, we designed the reverse path address code that allows an individual destination node to retrieve the reverse path address without searching the topology database and invoking any route computation program.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On a Class of Reversible Binary Cyclic Codes and their Algebraic Decoding

Abstract A class of reversible binary cyclic codes is presented together with an algebraic decoding algorithm that exploits their error correcting capabilities.

Reverse accumulation and attractive fixed points

We apply reverse accumulation to obtain automatic gradients and error estimates of functions which include in their computation a convergent iteration of the form y= Φ(y,u), where y and u are vectors. We suggest an implementation approach which allows this to be done by a fairly routine extension of existing reverse accumulation code. We show how to re-use the computational graph for the fixed point constructor Φ so as to set explicit stopping criteria for the iterations, based on the gradient accuracy required. Our construction allows the gradient vector to be obtained to the same order of accuracy as the objective function values (which is in general the best we can hope to achieve), and the same order of computational cost (which does not explicitly depend upon the number of independent variables.) The technique can be applied to functions which contain several iterative constructions, either serially or nested

Rocket plume radiation base heating by reverse Monte Carlo simulation

A reverse Monte Carlo radiative transfer code is developed to predict rocket plume base heating. It is more computationally efficient than the forward Monte Carlo method, because only the radiation that strikes the receiving point is considered. The method easily handles both gas and particle emission and particle scattering. Band models are used for the molecular emission spectra, and the Henyey-Greenstein phase function is used for the scattering. Reverse Monte Carlo predictions are presented for 1) a gas-only model of the Space Shuttle main engine plume; 2) a pure scattering plume with the radiation emitted by a hot disk at the nozzle exit; 3) a nonuniform temperature, scattering, emitting, and absorbing plume; and 4) a typical solid rocket motor plume. The reverse Monte Carlo method is shown to give good agreement with previous predictions. Typical solid rocket plume results show that 1) CO, radiation is emitted from near the edge of the plume; 2) H2O gas and A12O3 particles emit radiation mainly from the center of the plume; and 3) A12O3 particles emit considerably more radiation than the gases over the 400-17,000-cm spectral interval.

An improved Bombieri-Weil bound and applications to coding theory

Recently we obtained a sharpening of the Carlitz Uchiyama bound in characteristic two using Serre's improvement on Weil's estimate of the number of rational points on an algebraic curve over a finite field. In this paper we derive an improvement on a theorem of Bombieri and Weil. This has important applications in the theory of codes; for instance we obtain immediate results concerning the minimum distance of the dual of an arbitrary geometric Goppa code and the minimum distance of reversible BCH codes of length 2 m + 1.

On the generalized Hamming weights of several classes of cyclic cods

The generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. They were introduced by V.K. Wei (1991) and shown to characterize the performance of the linear code in certain cryptographical applications. Results are presented on the generalized Hamming weights of several classes of binary cyclic codes, including primitive double-error-correcting and triple-error-correcting BCH codes, certain reversible cyclic codes, and some extended binary Goppa codes. In particular, the second generalized Hamming weight of primitive double-error-correcting BCH codes is determined and upper and lower bounds are obtained for the generalized Hamming weights for the codes studied. These bounds are compared to results from other methods. >

Some properties of self-reciprocal polynomials

Self-Reciprocal Polynomials (SRP's) have applications in the construction of reversible error correcting codes, and the efficient implementation of linear feedback shift registers. Reversible codes are advantageous in certain data storage systems, where the data can be read in either direction. In this paper we extend previous results on SRP's. Specifically, the maximum possible exponent for a composite SRP over GF( q), q an odd prime, is derived, and a construction for these is given. A lower bound is given for the number of SRP's with this exponent. The maximum exponent for SRP's over GF(2) with certain degrees is also found.

The reverse genetic code: Specification of the doublet part

The reverse genetic code: Specification of the doublet part

A note on self-orthogonal codes

In this short note we give a new proof of Proposition 4.8 in Lander's book [2], which states that a self-orthogonal and reversible code is the zero-code. Our proof is much easier than the original one.

Variable‐length‐code‐selective reversible predictive coding for multilevel images

AbstractTo construct efficiently an image database system for high‐tone images, a variable‐length, code‐selective reversible predictive coding scheme with a high‐compression ratio is proposed. This coding scheme is based on application of the quantizer‐selective method in the DPCM coding [11] (previously proposed by the present authors) to an adaptive selection of a variable‐length code. This is an adaptive coding scheme in which a suitable code is selected from the pre‐designed variable‐length codes for each pel. This code selection method requires no additional information, since the code selection is carried out based only on information of pels for which the coding has already been completed. The predesigned variable‐length codes and the threshold values for the code selection are determined by a model of the probability distribution of transformed prediction‐error signals. The initial setting of coding parameters is constant and independent of the image to be encoded. This scheme has, therefore, much generality that is independent of any kinds of images. The coding rate of this scheme is improved by about 0.3 to 0.5 bit/pel compared with the optimal nonadaptive coding scheme using a single Huffman code. It was confirmed that the proposed scheme has the highest coding efficiency compared with several conventional representative reversible coding schemes.

Convenient construction of tetrahedral finite elements for the quasi-harmonic equation

It is shown that in the finite-element formulation of the general quasi-harmonic equation using tetrahedral elements, for every member of the element family there exists just one numerical universal matrix indpendent of the size, shape and material properties of the element. Thus the element matrix is conveniently constructed by manipulating this single matrix along with a set of reverse sequence codes at the same time accounting for the size, shape and material properties in a simple manner.

A transform approach to Goppa codes

Based on a finite Fourier transform of codewords over the finite field GF (q^{m}) , some basic properties of the class of Goppa codes are presented. A new lower bound on the minimum distance for these codes is derived and applied to a subclass of Goppa codes which is. in fact. equivalent to a subset of punctured reversible cyclic codes. Furthermore. it is shown how the class of Goppa codes can be easily decoded in the context of this transformation by using the Berlekamp-Massey decoding algorithm. Through a slight extension of the procedure, it is also shown how this algorithm may be used m decode alternant codes up to their guaranteed error-correction capability.