RESUMEN
Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718-7735, 2019), we define and study LRPC codes over Galois rings-a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.'s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above.
RESUMEN
The thermal decomposition of graphene oxide (GO) is a complex process at the atomic level and not fully understood. Here, a subclass of GO, oxo-functionalized graphene (oxo-G), was used to study its thermal disproportionation. We present the impact of annealing on the electronic properties of a monolayer oxo-G flake and correlated the chemical composition and topography corrugation by two-probe transport measurements, XPS, TEM, FTIR and STM. Surprisingly, we found that oxo-G, processed at 300 °C, displays C-C sp3 -patches and possibly C-O-C bonds, next to graphene domains and holes. It is striking that those C-O-C/C-C sp3 -separated sp2 -patches a few nanometers in diameter possess semiconducting properties with a band gap of about 0.4â eV. We propose that sp3 -patches confine conjugated sp2 -C atoms, which leads to the local semiconductor properties. Accordingly, graphene with sp3 -C in double layer areas is a potential class of semiconductors and a potential target for future chemical modifications.
RESUMEN
Synthesis and studies of graphite oxide started more than 150â years ago and turned into a boom by the measurements of the outstanding physical properties of graphene. A series of preparation protocols emanated trying to optimize the synthesis of graphene oxide in order to obtain a less defective material, as source for graphene. However, over-oxidation of the carbon framework hampered establishing structure-property relationships. Here, the fact that two different synthetic methods for graphene oxide preparation lead to very similar types of graphene oxide with a preserved graphene lattice is demonstrated. Either sodium chlorate in nitric acid (similar to Brodie's method) or potassium permanganate in sulfuric acid (similar to Hummers' method) treatment are possible; however, reaction conditions must be controlled. With a preserved carbon lattice analytical differences between the samples relate to the altered on-plane functionality. Consequently, terming preparation protocols "according to Brodie's/Hummers' method" is not sufficient.
RESUMEN
The electron source brightness is an important parameter of an electron microscope. Reliable and easy brightness measurement routes are not easily found. A determination method for the illumination semi-angle distribution in transmission electron microscopy is even less well documented. Herein, we report a facile measurement route for both entities and demonstrate it on a state-of-the-art instrument. The reduced axial brightness of the FEI X-FEG with a monochromator was determined to be larger than 108 A/(m2 sr V).