Recently, a new algebraic decoding method was proposed by Truong et al. In this paper, three decoders for the quadratic residue codes with parameters (71, 36, 11), (79, 40, 15), and (97, 49, 15), which have not been decoded before, are developed by using the decoding scheme given by Truong et al. To confirm our results, an exhaustive computer simulation was executed successfully.

A prime number p is called elite if only finitely many Fermat numbers 2 n + 1 are quadratic residues of p. Previously only the interval up to 10 was systematically searched for elite primes and 16 such primes were found. We extended this research up to 2.5 · 10 and found five further elites, among which 1 151 139 841 is the smallest and 171 727 482 881 the largest.

In the book which accompanies the stencils various methods of finding quadratic residues are discussed and the method by means of the expansion of the square root of the number in a continued fraction is found to be by far the most effective. Various examples are given illustrating the power of the stencils, and a reproduction of the first page of the list of primes accompanies the work. The pl...

In [1] a proof was given of Fermat’s Two-Square Theorem using the group theoretical structure of the classical modular group. This has been extended in many directions and to other square properties in general rings. In particular in [2] a two-square theorem was given for the Gaussian integers in terms of when ii is a quadratic residue. In this note we examine and survey this technique and the ...

Let π(x; d, a) denote the number of primes p ≤ x with p ≡ a(mod d). Chebyshev’s bias is the phenomenon that ‘more often’ π(x; d, n) > π(x; d, r), than the other way around, where n is a quadratic non-residue mod d and r is a quadratic residue mod d. If π(x; d, n) ≥ π(x; d, r) for every x up to some large number, then one expects that N(x; d, n) ≥ N(x; d, r) for every x. Here N(x; d, a) denotes ...

to study the effects of two irrigation regimes and application of barley residue, zeolite and superabsorbent polymer on forage yield and some physiological traits of maize and sorghum, an experiment was conducted over two years in kerman, iran. a randomized complete block design arranged in a factorial split was used with three replications. two irrigation regimes of normal irrigation and water...

abstract in order to study the sensitivity of seven crops to total herbicide soil residue, an experiment was carried out under controlled conditions in 2009 at the college of agriculture, ferdowsi university of mashhad-iran. in this study 7 crops (pea, bean, lentil, corn, rape, beet and tomato), across 7 simulated soil residual concentration of total herbicide (0, 0.0002, 0.0005, 0.001, 0.002, ...

to date, most studies have focused on continuous aerobic training and there is not comprehensive information about the influence of discontinuous aerobic training on cardiovascular risk biomarkers. taking this into consideration, the purpose of the present study is to investigate the influence of an 8-week discontinuous aerobic training program (3×10 min) on cardiovascular risk biomarkers in in...

In this paper, we develop stability, dissipativity, and optimality notions for dynamical systems with discontinuous vector fields. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps specifying a set of directions for the system velocity and admitting Filipp...