For any 4-regular graph G (possibly with multiple edges), we prove that, if the number N of distinct Euler orientations of G is such that N ≡ 1 (mod 3), then G has a 3-regular subgraph. It gives the new 4-regular graphs with multiple edges which have no 3-regular subgraphs, for which we know the number of Euler orientations.
— Optical orthogonal codes(OOC) are used as spreading sequences for optical CDMA networks. An OOC is a family of constant weight binary codes with a pre-specified maximum correlation parameter(MCP). Johnson in his 1962 paper introduced three bounds for constant weight codes, that we call bounds A, B, and Hybrid. Subsequently Chung et al. adapted Johnson… (More)
We establish a connection between finite fields and finite dynam-ical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
—New families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks are proposed. The families are based in the three dimensional periodic Welch Costas array over elementary Abelian groups. These new families are shown to be asymptotically optimal through the Johnson bound.