Weight distribution

A coding theory approach to error control in redundant residue number systems (RRNSs) is presented. The concepts of Hamming weight, minimum distance, weight distribution, and error detection and correction capabilities in redundant residue number systems are introduced. The necessary and sufficient conditions for the desired error control capability are derived from the minimum distance point of view. Closed-form expressions are

Poly(vinyl acetate-co-butyl acrylate) latexes having oligomeric N-methylol acrylamide were prepared by semi-continuous emulsion polymerization. The effects of new protective colloid and comonomer ratios on the physicochemical and colloidal properties of latexes were investigated. The changes in homopolymer and copolymer latexes were determined by measuring viscosity, particle size, molecular weight (MW), molecular weight distribution (MWD), and surface tension. \( \bar{M}_{n} \) values of copolymer latexes were found to be lower than the MWs of the poly(vinyl acetate) and poly(butyl acrylate) homopolymers. In general, \( \bar{M}_{n} \) and \( \bar{M}_{\text{w}} \) values of copolymer latexes changed irregularly with increasing BuA ratio in the copolymer composition.

In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting BCH code. Furthermore, for field extensions of F2 of odd degree, our results provide an alternative proof of the APN property of the functions.

On four-wheel-drive skidders (FWDS) the front and rear axles are rigidly coupled and the tyres are the same size. This means that angular speeds of the front and rear tyres are the same. Therefore, variations in the rolling radii of the front and rear tyres, due to changes in inflation pressure and tyre deflection, and different sinkage, etc., could cause significant torsional wind-up. A theoretical analysis and experiments showed that the coefficient of weight distribution influenced the efficiency of slip of a FWDS. In cases where the coefficient of weight distribution decreased, wheel slip was predicted and the ratio of the theoretical speed also increased leading to a loss of slip efficiency and the risk of torsional wind-up between both axles. Greater efficiency of slip was obtained with equal tyre inflation pressures in front and rear tyres. The efficiency of slip increased when tyre inflation pressures and drawbar pull were reduced. This can be explained by the fact that the ...

Abstract. We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well ...

The ecology of Holothuria fuscogilva was assessed in three habitats in the Republic of Maldives: marine grass beds, island gaps and lagoon floor. In the lagoon floor habitat, H. fuscogilva was the dominant sea cucumber with relative abundances ranging from 70 to 94.9% in the two atolls studied. In one island gap area the median density (biomass), movement and growth rate were 29 ha -1 (21 kg ha -1 ), 2 m d -1 and 0.29% d -1 , respectively. Based upon the weight distributions in the three habitats, H. fuscogilva appears to recruit to shallow marine grass beds, then migrates to deeper waters such as island gaps. It then moves to the deep waters of the lagoon floor, as it approaches sexual maturity (1.5 kg TW), where it matures and reproduces. Growth slows as the animal matures and individuals with total weights of 5000 g or greater were estimated to be at least 12 yrs old. Based upon micro and macroscopic examination of extracted gonads, mature individuals from the lagoon floor were f...

Search effectiveness metrics are used to evaluate the quality of the answer lists returned by search services, usually based on a set of relevance judgments. One plausible way of calculating an effectiveness score for a system run is to compute the inner-product of the run’s relevance vector and a “utility” vector, where the ith element in the utility vector represents

Network science has attracted much attention in recent years, primarily due to its application in many areas ranging from biology to medicine, engineering, and social sciences [1, 2]. Research in network science starts by observing a phenomenon in real data and then tries to construct models to mimic its behavior. Many real-world networks share some common structural properties such as scale-free degree distribution, small-worldness, and modularity. The dynamic behavior of networks largely depends on their structural properties [3, 4]. ...

Abstract. We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well ...

The ecology of Holothuria fuscogilva was assessed in three habitats in the Republic of Maldives: marine grass beds, island gaps and lagoon floor. In the lagoon floor habitat, H. fuscogilva was the dominant sea cucumber with relative abundances ranging from 70 to 94.9% in ...

We introduce a new approach for the study of weight distributions of cosets of the Reed-Muller code of order 1. Our approach is based on the method introduced by Kasami (1968), using Pless (1963) identities. By interpreting some equations, we obtain a necessary condition for a coset to have a “high” minimum weight. Most notably, we are able to distinguish such cosets which have three weights only. We then apply our results to the problem of the nonlinearity of Boolean functions. We particularly study the links between this criterion and the propagation characteristics of a function

The Hamming weight enumerator function of the formally self-dual even, binary extended quadratic residue code of prime p = 8m + 1 is given by Gleason's theorem for singly-even code. Using this theorem, the Hamming weight distribution of the extended quadratic residue is completely determined once the number of codewords of Hamming weight j Aj, for 0 j 2m, are known. The smallest prime for which the Hamming weight distribution of the corresponding extended quadratic residue code is unknown is 137. It is shown in this paper that, for p = 137 A2m = A34 may be obtained without the need of exhaustive codeword enumeration. After the remainder of Aj required by Gleason's theorem are computed and independently verified using their congru- ences, the Hamming weight distributions of the binary augmented and extended quadratic residue codes of prime 137 are derived.