High-speed polynomial basis multipliers over GF(2(m)) for special pentanomial.

Efficient hardware implementations of arithmetic operations in the Galois field are highly desirable for several applications, such as coding theory, computer algebra and cryptography. Among these operations, multiplication is of special interest because it is considered the most important building block. Therefore, high-speed algorithms and hardware architectures for computing multiplication are highly required. In this paper, bit-parallel polynomial basis multipliers over the binary field GF(2(m)) generated using type II irreducible pentanomials are considered. The multiplier here presented has the lowest time complexity known to date for similar multipliers based on this type of irreducible pentanomials.

First detection of the Sunyaev Zel'dovich effect increment at λ < 650 μm

The Sunyaev-Zel'dovich (SZ) effect is a spectral distortion of the cosmic microwave background as observed through the hot plasma in galaxy clusters. This distortion is a decrement in the CMB intensity for λ > 1.3 mm, an increment at shorter wavelengths, and small again by λ ~ 250 μm. As part of the Herschel Lensing Survey (HLS) we have mapped 1E0657–56 (the Bullet cluster) with SPIRE with bands centered at 250, 350 and 500 μm and have detected the SZ effect at the two longest wavelengths. The measured SZ effect increment central intensities are ΔI_0 = 0.097 ± 0.019 MJy sr^-1 at 350 μm and ΔI_0 = 0.268 ± 0.031 MJy sr^-1 at 500 μm, consistent with the SZ effect spectrum derived from previous measurements at 2 mm. No other diffuse emission is detected. The presence of the finite temperature SZ effect correction is preferred by the SPIRE data at a significance of 2.1σ, opening the possibility that the relativistic SZ effect correction can be constrained by SPIRE in a sample of clusters. The results presented here have important ramifications for both sub-mm measurements of galaxy clusters and blank field surveys with SPIRE.