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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)
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.
A new construction of arrays for watermarking is presented. The arrays are composed from cyclic shifts of a binary column with good autocor-relation. The sequence of shifts is obtained from a discrete logarithm of an irreducible quadratic over a finite field. This yields a large family of binary arrays with low off-peak autocorrelation and low… (More)