Abstract We study the structure of constacyclic codes of length ps over the ring Fpk + uFpk + · · · + um−1Fpk in terms of ideals in the quotient ring (Fpk + uFpk + · · · + um−1Fpk)[x]/〈xp s − λ〉, where λ is a unit element in Fpk + uFpk + · · · + um−1Fpk . In particular, we complete a structural classification of constacyclic codes of length ps over Fpk + uFpk and determine their minimum Hamming...

In this paper, we investigate cyclic code over the ring Fpk + vFpk + v 2 Fpk + ...+ v r Fpk , where v = v, p a prime number, r > 1 and gcd(r, p) = 1, we prove as generalisation of [9] that these codes are principally generated, give generator polynomial and idempotent depending on idempotents over this ring as response to an open problem related in [11]. we also give a gray map and proprieties ...

8 Forward position kinematics 20 8.1 General parallel structure . . . . . . . . . . . . . . . . . . . . . . 20 8.2 FPK by leg length error minimization . . . . . . . . . . . . . . . 21 8.3 Closed-form FPK for 321 structure . . . . . . . . . . . . . . . . . 22 8.4 Closed-form FPK: sensing redundancy . . . . . . . . . . . . . . . 24 ∗This Chapter uses material from the Chapters on Serial robots a...

Pairings over ellitpic curve use fields Fpk with p ≥ 2 and 6 < k ≤ 32. In this paper we propose to represent elements in Fp with AMNS sytem of [1]. For well chosen AMNS we get roots of unity with sparse representation. The multiplication by these roots are thus really efficient in Fp. The DFT/FFT approach for multiplication in extension field Fpk is thus optimized. The resulting complexity of a...

Pairings over ellitpic curve use fields Fpk with p ≥ 2 and 6 < k ≤ 32. In this paper we propose to represent elements in Fp with AMNS sytem of [1]. For well chosen AMNS we get roots of unity with sparse representation. The multiplication by these roots are thus really efficient in Fp. The DFT/FFT approach for multiplication in extension field Fpk is thus optimized. The resulting complexity of a...

The k-dimensional folded Petersen graph, FPk , is an iterative Cartesian product on the simple Petersen graph. As an essential component of folded Petersen cube, folded Petersen graph has many important properties. In this paper, we prove that the 3k-wide diameter and 3k-fault diameter of k-dimensional folded Petersen graph is either 2k + 1 or 2k + 2. Furthermore, we show that FPk is interval m...

A general formulation of the Fokker-Planck-Kolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHS). The FPK equation describes the time evolution of the probability law of the hybrid state. Our derivation is based on the concept of mean jump intensity, which is related to both the usual stochastic intensity (in t...

This article is devoted to investigating the evolution of probability density function for power system excited by fractional stochastic noise. First, single-machine-infinite-bus (SMIB) model Gaussian noise (FGN) established. Second, we derive Fokker–Planck–Kolmogorov (FPK) equation proposed and solve FPK using finite difference method. Finally, numerical results verify that addition FGN would ...

The forward position kinematics (FPK) of a parallel manipulator with new architecture supposed to be used as a moving mechanism in a flight simulator project is discussed in this paper. The closed form solution for the FPK problem of the manipulator is first determined. It has, then, been shown that there are at most 24 solutions for FPK problem. This result has been verified by using other tec...