Guangkui Xu

Two classes of p-ary bent functions and linear codes with three or four weights

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 Fp2k

Several classes of Boolean functions with few Walsh transform values

\mathbb {F}_{p^{2k}}

Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method

. Furthermore, the resulted p-ary bent functions are employed to construct a class of linear codes with three or four weights.

Further results on permutation polynomials of the form (xpm − x + δ)s + L(x) over 𝔽p2m

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 quadratic ones.

Recursive construction of optimal frequency-hopping sequence sets

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.

Some permutation pentanomials over finite fields with even characteristic

Several classes of permutation polynomials with given form over 𝔽p2m were recently proposed by Tu, Zeng, Li and Helleseth. In this paper, continuing their work, we present more permutation polynomials of the form (xpm − x + δ)s + L(x) over the finite field 𝔽p2m, where L(x) is a linearized polynomial with coefficients in 𝔽p.

Optimal Frequency-Hopping Sequence Sets Based on Cyclotomy

In this study, first the authors present a simplified representation of the Peng–Fan bounds on the periodic Hamming correlation of frequency-hopping sequence (FHS) sets, which may also be used to check the optimality of an FHS set with respect to the Peng–Fan bounds. Second, they propose a recursive construction of FHS sets from the known ones using some injective functions and the Chinese remainder theorem. It generalises the previous construction of optimal FHSs and FHS sets with composite lengths employing a given function. Without the limit of the specific function, their construction can produce new optimal FHSs and FHS sets that cannot be produced by the earlier construction. By choosing appropriate injective functions and known optimal FHSs and FHS sets, infinitely many new optimal FHSs and FHS sets can be recursively obtained.

Complete weight enumerators of a class of linear codes with two weights

Abstract Six classes of permutation pentanomials are constructed from fractional polynomials which permute the set of ( 2 m + 1 ) -th roots of unity. Based on an approach which is a generalization of the work of Zha, Hu and Fan, some permutation pentanomials and trinomials are also obtained from known permutations of the set of ( 2 m + 1 ) -th roots of unity.

Optimal FHSs and DSSs via near zero-difference balanced functions

In this paper, a kind of generalized cyclotomy with respect to the square of a prime is presented and the properties of the corresponding generalized cyclotomic numbers are investigated. Based on the generalized cyclotomy, a class of frequency-hopping sequence (FHS) set is constructed. By means of some basic properties of the generalized cyclotomy, we derive the Hamming correlation distribution of the new set. The results show that the proposed FHS set is optimal with regard to the average Hamming correlation (AHC) bound. By choosing suitable parameters, the construction also leads to the optimal FHS set and the optimal FHSs with regard to the maximum Hamming correlation (MHC) bound and Lempel-Greenberger bound, respectively.

Two classes of near-optimal frequency-hopping sequence sets with prime-power period

Abstract In this paper, a class of p -ary linear codes with two weights is constructed by using the properties of cyclotomic classes of F p 2 ∗ . The complete weight enumerators of these linear codes are also determined. In some cases, they are optimal and can be employed to obtain secret sharing schemes with interesting access structures and asymptotically optimal systematic authentication codes.