Construction of orthogonal CC-sets

Construction of amicable orthogonal design

This paper introduces some construction methods for amicable orthogonal designs over the real and quaternion domain which have not been explored for code design before. The proposed construction methods generate a large number of amicable orthogonal designs of quaternions. It is also shown that amicable orthogonal designs of quaternions can be used to construct restricted quaternion orthogonal ...

A Construction Method for Complete Sets of Mutually Orthogonal Frequency Squares

A construction is described for combining affine designs with complete sets of mutually orthogonal frequency squares to produce other complete sets.

Complete Sets of Orthogonal Self-Orthogonal Latin Squares

We show how to produce algebraically a complete orthogonal set of Latin squares from a left quasifield and how to generate algebraically a maximal set of self-orthogonal Latin squares from a left nearfield. For a left Veblen-Wedderburn system, we establish the algebraic relationships between the standard projective plane construction of a complete set of Latin squares, our projective plane cons...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Defining small sets from κ-cc families of subsets

We show that if X is a set and A is a non-empty family of n-element subsets of X that does not contain a pairwise disjoint family of cardinality strictly greater than k, then a non-empty subset of X of cardinality strictly less than kn is definable from A. We show that this result is nearly best possible, and investigate analogous questions for families of countable sets. We also study bounds o...