The main cryptographic features of Boolean functions when the input is restricted to some subset of F n 2 are studied recently because of the innovative stream cipher FLIP Méaux et al. (2016). In this paper, we propose a large family of Boolean functions which are (almost) balanced on every set of vectors in F n 2 \ {0, 1} with constant Hamming weight (the so-called weightwise (almost) perfectly balanced, W(A)PB). We show that these W(A)PB functions have optimal algebraic immunity on F n 2 and good algebraic immunity on some subsets of vectors in F n 2 , especially on the subsets of vectors with constant Hamming weight. This is the first time that W(A)PB functions with good local algebraic immunities are presented. Moreover, we discuss the nonlinearity and weightwise nonlinearity of these functions.
SUMMARYMulti-hypothesis prediction technique, which exploits inter-frame correlation efficiently, is widely used in block-based distributed compressive video sensing. To solve the problem of inaccurate prediction in multi-hypothesis prediction technique at a low sampling rate and enhance the reconstruction quality of non-key frames, we present a resamplebased hybrid multi-hypothesis scheme for block-based distributed compressive video sensing. The innovations in this paper include: (1) multihypothesis reconstruction based on measurements reorganization (MR-MH) which integrates side information into the original measurements; (2) hybrid multi-hypothesis (H-MH) reconstruction which mixes multiple multi-hypothesis reconstructions adaptively by resampling each reconstruction. Experimental results show that the proposed scheme outperforms the state-of-the-art technique at the same low sampling rate.
Keywords: strip roughness, non-rectangular meshes, relative spacing, resistance coefficient.
INTRODUCTIONThe flow over roughness boundary is one of the most interesting fluid motions in practical engineering. Therefore, many studies on the flow over rough boundary have been carried out experimentally and numerically by using various kinds of roughness elements. As we have known, discussing the turbulence structure of the flow over strip roughness is one of the approaches to understand the generation mechanism of turbulence in the flow over rough boundary. According to Knight and Macdonal1), the spacing between roughness elements has important influence on resistance coefficient compared with the height of roughness element for the flow over strip roughness; the resistance coefficient attains maximum when the relative spacing L/Hr defined as the ratio of the spacing L between the roughness elements and the roughness height Hr is from 6 to 10. If the relative spacing is smaller than 6, there are dead water regions between the roughness elements, and the height responded by the flow is smaller than the actual one; on the other hand, when the spacing of strip roughness is very large, it is easy to understand that resistance is smaller since the quantity of roughness elements is small in the total flow area. Because the boundaries around roughness elements are irregular due to the existence of circular roughness elements (see Fig. 1), special treatment near the solid wall is necessary. The body-fitted transformation is generally applied to treat irregular boundaries, but, after adopting the transformation, some additional terms will be put into the transformed
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