A Virtual Reality Application of the Rubber Hand Illusion Induced by Ultrasonic Mid-Air Haptic Stimulation

Ultrasonic mid-air haptic technologies, which provide haptic feedback through airwaves produced using ultrasound, could be employed to investigate the sense of body ownership and immersion in virtual reality (VR) by inducing the virtual hand illusion (VHI). Ultrasonic mid-air haptic perception has solely been investigated for glabrous (hairless) skin, which has higher tactile sensitivity than hairy skin. In contrast, the VHI paradigm typically targets hairy skin without comparisons to glabrous skin. The aim of this article was to investigate illusory body ownership, the applicability of ultrasonic mid-air haptics, and perceived immersion in VR using the VHI. Fifty participants viewed a virtual hand being stroked by a feather synchronously and asynchronously with the ultrasonic stimulation applied to the glabrous skin on the palmar surface and the hairy skin on the dorsal surface of their hands. Questionnaire responses revealed that synchronous stimulation induced a stronger VHI than asynchronous stimulation. In synchronous conditions, the VHI was stronger for palmar stimulation than dorsal stimulation. The ultrasonic stimulation was also perceived as more intense on the palmar surface compared to the dorsal surface. Perceived immersion was not related to illusory body ownership per se but was enhanced by the provision of synchronous stimulation

How to determine linear complexity and kk-error linear complexity in some classes of linear recurring sequences

Several fast algorithms for the determination of the linear complexity of $d$-periodic sequences over a finite field \F_q, i.e. sequences with characteristic polynomial $f(x) = x^d-1$, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial $f(x) = (x-1)^d$ for an arbitrary positive integer $d$, and $f(x) = (x^2+x+1)^{2^v}$ are presented. The result is then utilized to establish a fast algorithm for determining the $k$-error linear complexity of binary sequences with characteristic polynomial $(x^2+x+1)^{2^v}$

A Genetic Algorithm for Computing the k-Error Linear Complexity of Cryptographic Sequences

Some cryptographical applications use pseudorandom sequences and require that the sequences are secure in the sense that they cannot be recovered by only knowing a small amount of consecutive terms. Such sequences should therefore have a large linear complexity and also a large k-error linear complexity. Efficient algorithms for computing the kerror linear complexity of a sequence over a finite field only exist for sequences of period equal to a power of the characteristic of the field. It is therefore useful to find a general and efficient algorithm to compute a good approximation of the k-error linear complexity. In this paper we investigate the design of a genetic algorithm to approximate the k-error linear complexity of a sequence. Our preliminary experiments show that the genetic algorithm approach is suitable to the problem and that a good scheme would use a medium sized population, an elitist type of selection, a special design of the two point random crossover and a standard random mutation. The algorithm outputs an approximative value of the k-error linear complexity which is on average only 19.5% higher than the exact value. This paper intends to be a proof of concept that the genetic algorithm technique is suitable for the problem in hand and future research will further refine the choice of parameters

On the key equation over a commutative ring

We define alternant codes over a commutative ring R and a corresponding key equation. We show that when the ring is a domain, e.g. the p-adic integers, the error–locator polynomial is the unique monic minimal polynomial (shortest linear recurrence) of the syndrome sequence and that it can be obtained by Algorithm MR of Norton. When R is a local ring, we show that the syndrome sequence may have more than one (monic) minimal polynomial, but all the minimal polynomials coincide modulo the maximal ideal of R. We characterise the minimal polynomials when R is a Hensel ring. We also apply these results to decoding alternant codes over a local ring R: it is enough to find any monic minimal polynomial over R and to find its roots in the residue field. This gives a decoding algorithm for alternant codes over a finite chain ring, which generalizes and improves a method of Interlando et. al. for BCH and Reed–Solomon codes over a Galois ring