In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent functions.

In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $sum_{uin mathbb{F}_2^n,vin mathbb{F}_2^m}mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.

In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ2n to ℤq(q = 2m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.

As a with-carry analog (based on modular arithmetic) of the usual Walsh-Hadamard transform (WHT), arithmetic Walsh transform (AWT) has been used to obtain analogs of some properties of Boolean functions which are important in the design and analysis of cryptosystems. The existence of nonzero linear structure of Boolean functions is an important criterion to measure the weakness of these functions in their cryptographic applications. In this paper, we find more analogs of linear structures of Boolean functions from AWT. For some classes of n-variable Boolean functions f, we find necessary and sufficient conditions for the existence of an invariant linear structure and a complementary linear structure 1n of f. We abstract out a sectionally linear relationship between AWT and WHT of n-variable balanced Boolean functions f with linear structure 1n. This result show that AWT can characterize cryptographic properties of these functions as long as WHT can. In addition, for a diagonal Boolean function f, a recent result by Carlet and Klapper says that the AWT of f can be expressed in terms of the AWT of a diagonal Boolean function of algebraic degree at most 3 in a larger number of variables. We provide for the result a complete and more modular proof which works for both even and odd weights (of the parameter c in the Corollary 19 by Carlet and Klapper (DCC 73(2): 299-318, 2014).

This letter presents a novel memory-based architecture for radix-2 fast Walsh-Hadamard-Fourier transform (FWFT) based on the constant geometry FWFT algorithm. It is composed of a multi-function Processing Engine, a conflict-free memory addressing scheme and an efficient twiddle factor generator. The address for memory access and the control signals for stride permutation are formulated in detail and the methods can be applied to other memory-based FFT-like architectures.

We propose a practical method that acquires dense light transports from unknown 3D objects by employing orthogonal illumination based on a Walsh-Hadamard matrix for relighting computation. We assume the presence of color crosstalk, which represents color mixing between projector pixels and camera pixels, and then describe the light transport matrix by using sets of the orthogonal illumination and the corresponding camera response. Our method handles not only direct reflection light but also global light radiated from the entire environment. Tests of the proposed method using real images show that orthogonal illumination is an effective way of acquiring accurate light transports from various 3D objects. We demonstrate a relighting test based on acquired light transports and confirm that our method outputs excellent relighting images that compare favorably with the actual images observed by the system.

This paper presents an integer discrete cosine transform (IntDCT) with only dyadic values such as k/2n (k, n∈ in N). Although some conventional IntDCTs have been proposed, they are not suitable for lossless-to-lossy image coding in low-bit-word-length (coefficients) due to the degradation of the frequency decomposition performance in the system. First, the proposed M-channel lossless Walsh-Hadamard transform (LWHT) can be constructed by only (log2M)-bit-word-length and has structural regularity. Then, our 8-channel IntDCT via LWHT keeps good coding performance even if low-bit-word-length is used because LWHT, which is main part of IntDCT, can be implemented by only 3-bit-word-length. Finally, the validity of our method is proved by showing the results of lossless-to-lossy image coding in low-bit-word-length.

This paper is concerned with timing synchronization of high rates UWB signals operating in a dense multipath environment, where access must tackle inter-frame interference (IFI), inter-symbol interference (ISI) and even multi-user interference (MUI). A training-based joint timing and channel estimation scheme is proposed, which is resilient to IFI, ISI, MUI and pulse distortion. A low-complexity detection scheme similar to transmit-reference (TR) scheme comes out as a by-product. For saving the training symbols, we further develop an extended decision-directed (DD) scheme. A lower bound on the probability of correct detection is derived which agrees well with the simulated result for moderate to high SNR values. The results show that the proposed algorithm achieves a significant performance gain in terms of mean square error and bit error rate in comparison to the "timing with dirty templates" (TDT) algorithms.

This paper proposes an Orthogonal Frequency Division Multiplexing system with Grouping Adaptive Modulation method (GAM-OFDM). The salient feature of the proposed system is to enable the reduction of required transmission bits for adaptive modulation information (AMI) that is required in the demodulation process at the receiver. This paper also proposes an efficient AMI transmission method for the GAM-OFDM system to enable the efficient transmission of AMI bits by using only two preamble symbols, and the Multi-Carrier Spectrum Spreading (MC-SS) technique to achieve the excellent performance of AMI transmission even under severe multi-path fading environments. This paper presents the various computer simulation results to verify the performance of proposed GAM-OFDM system.