On the complete weight enumerators of some linear codes with a few weights

Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of linear codes are important research topics. In this paper, we consider some classes of linear codes with a few weights and determine the complete weight enumerators from which the corresponding Hamming weight distributions are derived with help of some sums involving Legendre symbol

Low-temperature synthesis and nanomagnetism of large-area α-Fe2O3 nanobelts

Large-area one dimensional (1D) α-Fe2O3 nanostructures were grown on iron substrates by catalyst-free thermal oxidation process at low temperatures in air. The structure characterization revealed that the nanostructures are single crystalline α-Fe2O3. Two kinds of α-Fe2O3 nanostructures, nanobelts and nanoflakes, were obtained due to the different growth temperature range. A surface diffusion mechanism is proposed to account for the nanobelts and nanoflakes growth. The Morin temperature TM of pure 1D α-Fe2O3 nanostructures is 121 K, which is far below their bulk counterparts. The coercive field depends on temperature, and takes values 471 Oe at 5 K and about 260 Oe when the temperature is greater than TM , respectively