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Multi-Edge type Low-Density Parity-Check codes (MET-LDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we drive ACWD of MET-LDPC code ensembles from ACWD of their constituent ensembles.

In this paper, we explicitly formulate the average weight and the stopping set distributions and their asymptotic exponents of two-edge type LDPC code ensembles. We also show some characteristics such as the symmetry and the conditions for zero of the weight distributions of two code ensembles. Further we investigate the relation between two code ensembles from the perspectives of the weight and stopping set distributions.

Third-order nonlinear optical properties of multinuclear organometallic complexes consisting of metal–metal multiple bonds previously studied by picosecond degenerate four-wave mixing (DFWM) are reexamined by femtosecond optical heterodyned optical Kerr effect (OHD-OKE) and femtosecond Z-scan techniques. The real part of off-resonant second hyperpolarizabilities are obtained at a wavelength of 1280 nm to be +3.0 ± 10−33 esu for a Pt–Mo–Mo–Pt tetranuclear complex and less than 10−33 esu for a Mo–Mo dinuclear complex. The present results clarify that the previously reported values are not off-resonant values and the off-resonant property of the tetranuclear complex is superior to that of the dinuclear one.