Orthogonal Designs and a Cubic Binary Function

[hal-00864648, v1] Orthogonal designs and a cubic binary function

Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is to construct designs maximizing the rate and minimizing the decoding delay. All known constructions of CODs are inductive or algorithmic. In this paper, we ...

Tabulation of cubic function fields via polynomial binary cubic forms

We present a method for tabulating all cubic function fields over Fq(t) whose discriminant D has either odd degree or even degree and the leading coefficient of −3D is a non-square in Fq , up to a given bound B on deg(D). Our method is based on a generalization of Belabas’ method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport an...

Orthogonal stability of mixed type additive and cubic functional equations

In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.

Construction of Orthogonal and Nearly Orthogonal Latin Hypercube Designs from Orthogonal Designs

Latin hypercube designs (LHDs), widely used for computer experiments, are a very large class of designs with desirable properties. Recently, a number of methods have been proposed to construct orthogonal LHDs. In this paper, we introduce an approach to constructing 2-order orthogonal designs. The methods are simple and easy to implement. Using orthogonal designs, we propose some methods for con...

Generalized orthogonal designs