• Constructing APN functions through isotopic shifts 

      Budaghyan, Lilya; Calderini, Marco; Carlet, Claude; Coulter, Robert; Villa, Irene (Journal article; Peer reviewed, 2020)
      Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, mathematics and information theory. In this paper we deduce a new method ...
    • 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 Asymptotics of Solving the LWE Problem Using Coded-BKW With Sieving. 

      Guo, Qian; Johansson, Thomas; Mårtensson, Erik; Wagner, Paul Stankovski (Peer reviewed; Journal article, 2019)
    • On the Classification of Hermitian Self-Dual Additive Codes over GF(9) 

      Danielsen, Lars Eirik (Peer reviewed; Journal article, 2012-08)
      Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. ...
    • 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 ...
    • 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 ...