Kathy J. Horadam

Cocyclic Hadamard codes

We demonstrate that many well-known binary, quaternary, and q-ary codes are cocyclic Hadamard codes; that is, derived from a cocyclic generalized Hadamard matrix or its equivalents. Nonlinear cocyclic Hadamard codes meet the generalized Plotkin bound. Using presemifield multiplication cocycles, we construct new equivalence classes of cocyclic Hadamard codes which meet the Plotkin bound.

Retina Verification System Based on Biometric Graph Matching

This paper presents an automatic retina verification framework based on the biometric graph matching (BGM) algorithm. The retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators. Then, retinal templates are defined as formal spatial graphs derived from the retinal vasculature. The BGM algorithm, a noisy graph matching algorithm, robust to translation, non-linear distortion, and small rotations, is used to compare retinal templates. The BGM algorithm uses graph topology to define three distance measures between a pair of graphs, two of which are new. A support vector machine (SVM) classifier is used to distinguish between genuine and imposter comparisons. Using single as well as multiple graph measures, the classifier achieves complete separation on a training set of images from the VARIA database (60% of the data), equaling the state-of-the-art for retina verification. Because the available data set is small, kernel density estimation (KDE) of the genuine and imposter score distributions of the training set are used to measure performance of the BGM algorithm. In the one dimensional case, the KDE model is validated with the testing set. A 0 EER on testing shows that the KDE model is a good fit for the empirical distribution. For the multiple graph measures, a novel combination of the SVM boundary and the KDE model is used to obtain a fair comparison with the KDE model for the single measure. A clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60% and more than two orders of magnitude.

Cocyclic Hadamard matrices and difference sets

Abstract This paper locates cocyclic Hadamard matrices within the mainstream of combinatorial design theory. We prove that the existence of a cocyclic Hadamard matrix of order 4t is equivalent to the existence of a normal relative difference set with parameters (4t,2,4t,2t) . In the basic case we note there is a corresponding equivalence between coboundary Hadamard matrices and Menon–Hadamard difference sets. These equivalences unify and explain results in the theories of Hadamard groups, divisible designs with regular automorphism groups, and periodic autocorrelation functions.

Generation of Cocyclic Hadamard Matrices

The theory of cocyclic development of designs is applied to binary matrices, and an algorithm for generating cocyclic binary matrices is outlined. The eventual goal is to generate and classify all cocyclic Hadamard matrices of small side, in terms of an underlying group G and a cocycle f : G × G → Z 2. Preliminary results are presented and open problems are posed.

Cocyclic Generalised Hadamard Matrices and Central RelativeDifference Sets

AbstractCocyclic matrices have the form

Codes from Cocycles

M = [\psi (g,h)]_{g,h} \in G,

Community Detection in Bipartite Networks: Algorithms and Case studies

where G is a finite group, C is a finite abelian group and ψ : G × G → C is a (two-dimensional) cocycle; that is,