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—In this paper, several new classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions. Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all… (More)

The switching method is a very powerful method to construct new APN functions and differentially 4-uniform permutations over finite fields of even characteristic. In this paper, using this method, we present several new constructions of infinite classes of nonpower APN functions and two new classes of bent functions in finite fields of odd characteristic.

In this paper, a secondary construction of p-ary bent functions is presented. Two classes of p-ary bent functions of algebraic degree p are constructed by modifying the values of some known bent functions on some set of F p 2 k $\mathbb {F}_{p^{2k}}$ . Furthermore, the resulted p-ary bent functions are employed to construct a class of linear codes with… (More)

In this paper, several classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions. Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known… (More)

For any odd prime p≥5, some optimal p-ary cyclic codes with parameters [p m −1,p m −2m−2,4] are presented by using perfect nonlinear monomials and the inverse function over 𝔽 p m $\mathbb {F}_{p^{m}}$ . In addition, almost perfect nonlinear monomials, and other monomials over 𝔽 5 m $\mathbb {F}_{5^{m}}$ are used to construct optimal quinary cyclic codes… (More)

In this paper, two infinite classes of quadratic differentially p-uniform binomials over $$\mathbb {F}_{p^n}$$ F p n (n is divisible by 4 or 3) are constructed from known perfect nonlinear binomials. In particular, for $$p=3$$ p = 3 , such functions are ternary differentially 3-uniform functions which are not CCZ-equivalent to known ones. In addition, two… (More)

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