Sets constructed by acceptors

Perfect difference sets constructed from Sidon sets

A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...

Two Level Cretan Matrices Constructed via Singer Difference Sets

Two Level Cretan Matrices Constructed via Singer Difference Sets N. A. Balonin and Jennifer Seberry† October 4, 2014 We show that if B is the incidence matrix of a (υ, k, λ) difference set, then there exists a two-level quasi-orthogonal matrix, S, a Cretan(υ) matrix. We apply this result to the Singer family of difference sets obtaining a new infinite family of Cretan matrices.

On the Dimensions of Certain Incommensurably Constructed Sets

Orthogonal sets of data windows constructed from trigonometric polynomials

In contrast to common practise in many other physical sciences, the statistical analysis of PTTI data is often based directly on time domain techniques rather than on frequency domain (spectral analysis) techniques. The predominant analysis technique in the PTTI community, namely, the two-sample (or Allan) variance, is often used to indirectly infer frequency domain properties under the assumpt...

On a Class of Almost Difference Sets Constructed by Using the Ding-Helleseth-Martinsens Constructions

Pseudorandom binary sequences with optimal balance and autocorrelation have many applications in stream cipher, communication, coding theory, etc. It is known that binary sequences with three-level autocorrelation should have an almost difference set as their characteristic sets. How to construct new families of almost difference set is an important research topic in such fields as communicatio...