• Binary Linear Codes With Few Weights From Two-to-One Functions 

      Li, Kangquan; Li, Chunlei; Helleseth, Tor; Qu, Longjiang (Journal article; Peer reviewed, 2021)
      In this paper, we apply two-to-one functions over b F 2n in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) (x 2t +x) e with ...
    • Cryptographically strong permutations from the butterfly structure 

      Li, Kangquan; Li, Chunlei; Helleseth, Tor; Qu, Longjiang (Journal article; Peer reviewed, 2021)
      Boomerang connectivity table is a new tool to characterize the vulnerability of cryptographic functions against boomerang attacks. Consequently, a cryptographic function is desired to have boomerang uniformity as low as ...
    • The differential spectrum of a ternary power mapping 

      Xia, Yongbo; Zhang, Xianglai; Li, Chunlei; Helleseth, Tor (Journal article; Peer reviewed, 2020)
      A function f(x)from the finite field GF(pn)to itself is said to be differentially δ-uniform when the maximum number of solutions x ∈GF(pn)of f(x +a) −f(x) =bfor any a ∈GF(pn)∗and b ∈GF(pn)is equal to δ. Let p =3and d =3n−3. ...
    • The Differential Spectrum of the Power Mapping xpn−3 

      Yan, Haode; Xia, Yongbo; Li, Chunlei; Helleseth, Tor; Xiong, Maosheng; Luo, Jinquan (Journal article; Peer reviewed, 2022)
      Let n be a positive integer and p a prime. The power mapping xpn−3 over Fpn has desirable differential properties, and its differential spectra for p=2,3 have been determined. In this paper, for any odd prime p , by ...
    • Encoding and decoding of several optimal rank metric codes 

      Kadir, Wrya Karim Kadir; Li, Chunlei; Zullo, Ferdinando (Journal article; Peer reviewed, 2022)
      This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation ...
    • Further investigations on permutation based constructions of bent functions 

      Li, Kangquan; Li, Chunlei; Helleseth, Tor; Qu, Longjiang (Journal article; Peer reviewed, 2023)
      Constructing bent functions by composing a Boolean function with a permutation was introduced by Hou and Langevin in 1997. The approach appears simple but heavily depends on the construction of desirable permutations. In ...
    • Interpolation-based Decoding of Nonlinear Maximum Rank Distance Codes 

      Li, Chunlei (Peer reviewed; Journal article, 2019)
      In this paper, we formulate a generic construction of MRD codes that covers almost all the newly found MRD codes. Among those MRD codes, we particularly investigate the encoding and decoding of a family of nonlinear MRD ...
    • On decoding additive generalized twisted Gabidulin codes 

      Kadir, Wrya; Li, Chunlei (Journal article; Peer reviewed, 2020)
      In this paper, we consider an interpolation-based decoding algorithm for a large family of maximum rank distance codes, known as the additive generalized twisted Gabidulin codes, over the finite field Fqn for any prime ...
    • On interpolation-based decoding of a class of maximum rank distance codes 

      Kadir, Wrya Karim Kadir; Li, Chunlei; Zullo, Ferdinando (Journal article; Peer reviewed, 2021)
      In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with ...
    • Optimal ternary cyclic codes with minimum distance four and five 

      Li, Nian; Li, Chunlei; Helleseth, Tor; Ding, Cunsheng; Tang, Xiaohu (Journal article, 2014-11)
      Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are ...
    • Sequences and Linear Codes from Highly Nonlinear Functions 

      Li, Chunlei (Doctoral thesis, 2014-06-16)
      Due to optimal nonlinearity and differential uniformity, perfect nonlinear (PN) and almost perfect nonlinear (APN) functions are of great importance in cryptography. It is interesting that they also define optimal objects ...
    • Two New Families of Quadratic APN Functions 

      Li, Kangquan; Zhou, Yue; Li, Chunlei; Qu, Longjiang (Journal article; Peer reviewed, 2022)
    • The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials 

      Li, Chunlei; Li, Nian; Helleseth, Tor; Ding, Cunsheng (Peer reviewed; Journal article, 2014-08)
      Let m ≥ 3 be an odd integer and p be an odd prime. In this paper, a number of classes of three-weight cyclic codes C(1,e) over Fp, which have parity-check polynomial m1(x)me (x), are presented by examining general conditions ...