TraceabilityCodes are CombinatorialObjects introduced by Chor, Fiat and Naor in 1994[7] to be used traitor tracing protect Digital Content. Frameproof Codes were given byBoneh Shaw 1994 prevent privacy gave the idea of c-secure codes withέ-error. Traceable is a strong form Codes. Balanced Incomplete Block Design frameproof arealready available literature [4]. Here this paper we will define how ...

Veevers and Boffey [1] identified 12 elementary balanced arrays. Zafar-Yab [2] confirmed the results of Veevers and Boffey [1] and investigated that among those 12 arrays, six arrays are unique and the other six are their associate partners. In this paper, there are 54 isomorphic classes containing 43-hills. Among these arrays 12 are vertically self-buildable arrays, after suitably augmentation...

A new method is presented for calculating the elements of T′T, of an array T in two symbols. The concept of marginal index is introduced. It is proved that the elements of T′T can be written in terms of marginal indices. A theorem is presented for the case of Partially Balanced array and its generalization for PB1 and Extended PB1 arrays. This method is useful in calculating the information mat...

In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value −1 within LCZ.

Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency c...

Polygonal designs, a class of partially balanced incomplete block designs with regular polygons, are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs) when neighboring units in a population provide similar information. In this paper, the method of cyclic shifts is used and cyclic polygonal...

We generalize chain enumeration in graded partially ordered sets by relaxing the graded, poset and Eulerian requirements. The resulting balanced digraphs, which include the classical Eulerian posets having an R-labeling, implies the existence of the (non-homogeneous) cd-index, a key invariant for studying inequalities for the flag vector of polytopes. Mirroring Alexander duality for Eulerian po...

Designing spaces that are able to balance illumination, glare and solar gains over a whole year is a real challenge, yet a problem faced every day by building envelope designers. To assist them in this search, a full year, climate-based daylighting simulation method was developed, called Lightsolve, meant to be used early on in the design process when façade and space details have not yet been ...