• 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. ...
    • A New Family of APN Quadrinomials 

      Budaghyan, Lilya; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2020)
      The binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified ...
    • On the Distance Between APN Functions 

      Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2020)
      We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize ...
    • 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 ...
    • Relation between o-equivalence and EA-equivalence for Niho bent functions 

      Davidova, Diana; Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor; Ihringer, Ferdinand; Penttila, Tim (Journal article; Peer reviewed, 2021)
      Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent ...
    • 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 ...