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Introduced by Rothaus in 1976 as interesting combinatorial objects, bent functions are maximally nonlinear Boolean functions with even numbers of variables whose Hamming distance to the set of all affine functions equals 2n−1 ± 2 n 2 −1. Not only bent functions are applied in cryptography, such as applications in components of S-box, block cipher and stream(More)
The study showed that in solar greenhouse continuously cropped cucumber soil, phenolic acids p-hydroxybenzoic acid, ferulic acid and benzoic acid had an obvious accumulation with increasing cropping year, and their contents were significantly higher after continuously cropped for 5 approximately 9 years than for 1 approximately 3 years. With the increasing(More)
Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes have been studied for many years and find many applications. The determination of the weight distributions of such codes is an open problem. Generally, the weight distributions of cyclic codes are difficult to determine. Utilizing a class of(More)
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Non-binary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. In(More)
Linear codes with a few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. and Zhou et al. to general weakly regular bent(More)
Linear codes can be applied in secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper generalizes the construction of linear codes by Ding et al. [9], uses more flexible construction method, and presents linear codes with few weights. These codes contain twoweight linear codes, one-weight linear codes, and(More)
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Non-binary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. On the(More)
In this paper we investigate properties of generalized bent Boolean functions and 2-bent (i.e., negabent, octabent, hexadecabent, et al.) Boolean functions in a uniform framework. We generalize the work of Stǎnicǎ et al., present necessary and sufficient conditions for generalized bent Boolean functions and 2-bent Boolean functions in terms of classical(More)
In this paper, we present a new class of semi-bent quadratic Boolean functions of the form f(x) = ∑⌊m−1 2 ⌋ i=1 Tr n 1 (cix 1+4i) (ci ∈ F4,n = 2m). We first characterize the semi-bentness of these quadratic Boolean functions. There exists semi-bent functions only when m is odd. For the case: m = p, where p is an odd prime with some conditions, we enumerate(More)