During the past few years we have obtained several new computer classification results on association schemes and in particular distance regular and strongly regular graphs. Central to our success is the use of two algebraic constraints based on properties of the minimal idempotents Ei of these association schemes : the fact that they are positive semidefinite and that they have known rank. Inc...

We study binary linear codes constructed from fifty-four Hadamard 2-(71, 35, 17) designs. The constructed codes are self-dual, doubly-even and self-complementary. Since most of these codes have large automorphism groups, they are suitable for permutation decoding. Therefore we study PD-sets of the obtained codes. We also discuss the errorcorrecting capability of the obtained codes by majority l...

Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and Gaborit Quadratic Double Circulant codes ...

We combine Steiner systems with Hadamard matrices to produce a new class of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph.

Let G be a graph of order n and let μ be an eigenvalue of multiplicity m. A star complement for μ in G is an induced subgraph of G of order n −m with no eigenvalue μ. In this paper, we study maximal and regular graphs which have Kr,s + tK1 as a star complement for 1 as the second largest eigenvalue. It turns out that some well known strongly regular graphs are uniquely determined by such a star...

SRG Action: Impact/Priority Score: 30 Human Subjects: 30-Human subjects involved Certified, no SRG concerns Animal Subjects: 30-Vertebrate animals involved no SRG concerns noted Gender: 3A-Only men, scientifically acceptable Minority: 1A-Minorities and non-minorities, scientifically acceptable Children: 1A-Both Children and Adults, scientifically acceptable Clinical Research not NIH-defined Pha...

In this presentation a technique for constructing bent functions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd dimension. This type of functions yield the first k...

We have studied light-induced birefringence (LIB) and surface relief grating (SRG) formation in the series of methylacrylate polymers. The effect of material structure such as length of photochromic side chain, glass transition temperature and molecular structure of azo units on LIB and SRG are studied. The optical formation of self-induced SRG on films of these materials is also presented.

We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymptotically represented by a formal power series in the perturbation parameter. The geometry of the problem and the nature of the elements involved in it give rise to different asymptotic levels related to the so-called...

The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some optimal codes, which meets certain bound on linear codes. The dual codes are also studied and proved to be optimal or almost optimal. These codes may have appli...