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Some results about the cross-correlation function between two maximal linear sequences
  • T. Helleseth
  • Computer Science, Mathematics
    Discret. Math.
  • 1 November 1976
The values and the number of occurences of each value of Cd(t) for several new values of d are determined for several different periods of period pn − 1.
Monomial and quadratic bent functions over the finite fields of odd characteristic
The (weak) regularity of the new as well as of known monomial bent functions is discussed, the first example of a not weakly regular bent function is given and some criteria for an arbitrary quadratic function to be bent are proven.
Almost difference sets and their sequences with optimal autocorrelation
A well-rounded treatment of known families of almost difference sets is given, relations between some difference sets and some almost difference Sets are established, and the numerical multiplier group of some families ofalmost difference sets are determined.
New Generalized Cyclotomy and Its Applications
In this paper we first introduce a new generalized cyclotomy of order 2 with respect tope11···pett, then we calculate the new cyclotomic numbers of order 2. Some applications of the new cyclotomy in
Several classes of binary sequences with three-level autocorrelation
In this correspondence, several classes of binary sequences with three-level autocorrelation are described, based on cyclic almost difference sets, which have optimum autOCorrelation.
On the minimum distance of array codes as LDPC codes
This correspondence investigates the minimum distance d(q,j) of the code in an algebraic way and proves that the code is invariant under a doubly transitive group of "affine" permutations.
New families of binary sequences with optimal three-level autocorrelation
Several new families of binary sequences of period N with optimal three-level autocorrelation, where N/spl equiv/2 (mod 4) is given, either balanced or almost balanced.
Optimal Ternary Cyclic Codes From Monomials
  • C. Ding, T. Helleseth
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 30 April 2013
Almost perfect nonlinearmonomials, and a number of other monomials over GF(3m) are used to construct optimal ternary cyclic codes with the same parameters.
A New Attack on the Filter Generator
The filter generator is an important building block in many stream ciphers. The generator consists of a linear feedback shift register of length n that generates an m-sequence of period 2n-1 filtered