It is known that under certain conditions the incidence matrix of a balanced incomplete block design (v, b, r, k, λ) gives a binary code of length b and size 2(v + 1). Here we investigate the conditions where a balanced ternary design gives a similar ternary code.

Andersson introduced general balanced trees, search trees based on the design principle of partial rebuilding: perform update operations naively until the tree becomes too unbalanced, at which point a whole subtree is rebalanced. We define and analyze a functional version of general balanced trees which we call root-balanced trees. Using a lightweight model of execution time, amortized logarith...

A structural analysis and classification of the reaction networks of the multiroute reactions is made using the bipartite graph method. Simple submechanisms of the overall reaction mechanism are defined, so as to correspond to routes with minimal stoichiometric numbers. The possibility for balancing the intermediate species is advocated as the major classificational criterion which discriminate...

We prove Ramsey-type results for intersection graphs of geometric objects the plane. In particular, we prove the following bounds, all of which are tight apart from the constant c. There is a constant c > 0 such that for every family F of n ≥ 2 convex sets in the plane, the intersection graph of F or its complement contains a balanced complete bipartite graph of size at least cn. There is a con...

In this paper, we partially solve an open problem, due to J. C. Molluzzo in 1976, on the existence of balanced Steinhaus triangles modulo a positive integer n, that are Steinhaus triangles containing all the elements of Z/nZ with the same multiplicity. For every odd number n, we build an orbit in Z/nZ, by the linear cellular automaton generating the Pascal triangle modulo n, which contains infi...

1 I n t r o d u c t i o n It is well known that the resistance of a product cipher to modern cryptanalytic attacks such as linear and differential cryptanalysis [10,1] depends critically upon the nonlinearity of the Boolean functions comprising the round function. Typically these functions must be balanced, so there is considerable interest in the design of highly nonlinear balanced Boolean fun...

A multi-objective optimum design method of the balanced Surface Acoustic Wave (SAW) filter is proposed. The frequency response characteristics of the balanced SAW filters are governed primarily by their geometrical structures. Besides, specifications for a balanced SAW filter is given by using several criteria. Therefore, in order to realize desirable frequency response characteristics, the str...

Optical signal processing devices based on quasi-phase-matched three-wave mixing and cascaded three-wave mixing in guided-wave geometries have been demonstrated to operate efficiently at practical pump-power levels. We describe operation of such devices in a balanced mode that allows mixing without wavelength offset and separation of mixed output from pump and signal input without wavelength-se...

A Boolean function f satis es PC(l) of order k if f(x) f(x ) is balanced for any such that 1 W ( ) l even if any k input bits are kept constant, where W ( ) denotes the Hamming weight of . This paper shows the rst design method of such functions which provides deg(f) 3. More than that, we show how to design \balanced" such functions. High nonlinearity and large degree are also obtained. Further...