Generalized Hamming Weights of Cyclic Codes from Algebraic Function Fields

The generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. In this paper, some results are presented on the estimates of generalized Hamming weights of cyclic codes, which connect their corresponding trace codes.

Nanosphere Lithography: Self-Assembled Photonic and Magnetic Materials

Early work with size-tunable periodic particle arrays (PPAs) fabricated by nanosphere lithography (NSL) demonstrated that the localized surface plasmon resonance (LSPR) could be tuned throughout the visible region of the spectrum. Further developments of the NSL technique have produced a myriad of nanoparticle configurations. Presented in this paper are several array types and examples of their utility in current applications. Both the sensitivity and tunability of the LSPR have been firmly established using single layer PPAs. Magnetic force microscopy (MFM) has been used to show that double layer PPAs act as single domain magnets and give strong MFM contrast. Angle-resolved NSL has produced nanogap and nano-overlap structures with manipulation resolution of one nanometer. Nanowell structures extend the original twodimensional structure into the third dimension. Exploitation of this flexible, materials-general NSL technique allows for investigation of the catalytic, electrochemical, magnetic, optical and thermodynamic properties of nanoparticles.