• 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 ...
    • Bounds on the nonlinearity of differentially uniform functions by means of their image set size, and on their distance to affine functions 

      Carlet, Claude Michael (Journal article; Peer reviewed, 2021)
      We revisit and take a closer look at a (not so well known) result of a 2017 paper, showing that the differential uniformity of any vectorial function is bounded from below by an expression depending on the size of its image ...
    • The Connections Among Hamming Metric, b-Symbol Metric, and r-th Generalized Hamming Metric 

      Shi, Minjia; Zhu, Hongwei; Helleseth, Tor (Journal article; Peer reviewed, 2023)
      The r -th generalized Hamming metric and the b -symbol metric are two different generalizations of Hamming metric. The former is used on the wire-tap channel of Type II, and the latter is motivated by the limitations of ...
    • 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 ...
    • Covering Radius of Generalized Zetterberg Type Codes Over Finite Fields of Odd Characteristic 

      Shi, Minjia; Helleseth, Tor; Özbudak, Ferruh (Journal article; Peer reviewed, 2023)
      Let Fq0 be a finite field of odd characteristic. For an integer s≥1 , let Cs(q0) be the generalized Zetterberg code of length qs0+1 over Fq0 . If s is even, then we prove that the covering radius of Cs(q0) is 3. Put q=qs0 ...
    • 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 ...
    • 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 ...
    • New Results on the -1 Conjecture on Cross-Correlation of m-Sequences Based on Complete Permutation Polynomials 

      Wu, GaoFei; Feng, Keqin; Li, Nian; Helleseth, Tor (Journal article; Peer reviewed, 2023)
      The cross-correlation between two maximum length sequences (m-sequences) of the same period has been studied since the end of 1960s. One open conjecture by Helleseth states that the cross- correlation between any two p-ary ...
    • 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 ...
    • On Two Fundamental Problems on APN Power Functions 

      Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael; Davidova, Diana; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2022)
      The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open ...
    • 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 ...