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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 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)
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)
Bent functions, which are maximally nonlinear Boolean functions with even numbers of variables and whose Hamming distance to the set of all affine functions equals 2 n−1 ± 2 n 2 −1 , were introduced by Rothaus in 1976 when he considered problems in combinatorics. Bent functions have been extensively studied due to their applications in cryptography, such as(More)
—Introduced by Rothaus in 1976 as interesting combi-natorial objects, bent functions are maximally nonlinear Boolean functions with even numbers of variables whose Hamming distance to the set of all affine functions equals 2 n−1 ± 2 n 2 −1. Not only bent functions are applied in cryptography, such as applications in components of S-box, block cipher and(More)
Bent functions, which are maximally nonlinear Boolean functions with even numbers of variables and whose Hamming distance to the set of all affine functions equals 2 n−1 ± 2 n 2 −1 , were introduced by Rothaus in 1976 when he considered problems in combinatorics. Bent functions have been extensively studied due to their applications in cryptography, such as(More)
Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014) constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open(More)