Difference Systems of Sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cyclic difference sets was introduced in [6] and applied to cyclic difference sets (n, (n−1)/2, (n−3)/4) of Paley type, where n ≡ 3 (mod 4) is a prime number. This paper develops similar constructions for prime numbers n ≡ ...

In this paper we present a family of ternary quasi-perfect BCH codes. These codes are of minimum distance 5 and covering radius 3. The first member of this family is the ternary quadratic-residue code of length 13.

Let n ∈ N and let A ⊆ Z/nZ be such that A does not contain 0 and it is non–empty. Generalizing a well known constant, EA(n) is defined to be the least t ∈ N such that for all sequences (x1, . . . , xt) ∈ Z, there exist indices j1, . . . , jn ∈ N, 1 ≤ j1 < · · · < jn ≤ t, and (θ1, · · · ,θn) ∈ A with ∑n i=1 θixji ≡ 0 (mod n). Similarly, for any such set A, we define the Davenport Constant of Z/n...

In this paper, we study explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression. We also refine the classical conditional bounds of Littlewood for L-functions at s = 1. In part...

— For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z to congruences ax+ by ≡ 0 mod q.

The free action for the massless sector of the Type II superstring was recently constructed using closed RNS superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N=2 D=10 SUSY algebra with Ramond-Ramond

In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes share similar properties with quadratic residue codes over finite fields. For the case p = 2, Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two...

a 2-years (2007-2009) field study was carried out at the college of agriculture, shiraz university, to evaluate the influence of crop residues management and nitrogen (n) rates on soil quality and barley grain protein under dryland conditions. the experiment was conducted as strip split plot with four replications. horizontal plots were three crop residues rates (0, 750 and 1500 kg ha-1), verti...

one method of seed placement into the soil as regards no-till system is the use of punch planting by which one can plant through a considerable depth of surface residue. the study was conducted using a 2?3 split-plot experimental design of three replications. the factors considered were two types of plantes (conventional planter vs. hinging pneumatic punch planter) and three levels of wheat res...

the effects of soil tillage methods and residue management were studied at miandoab agriculure station during 2003-2005. the experiment design was split block with the main plots devoted to residual management strategies (burning residue, crushing residue by disk, no treatment). subplots were tillage methods (moldboard plowing to 20-25 cm in fall, moldboard plowing to 20-25 cm in spring, moldbo...