Generating and counting binary bent sequences

Two general classes of binary bent sequences, bent-based and linear-based, are introduced. Algorithms that allow easy generation of bent sequences from either class are given. Based on some simple computation and a computer search, the authors conjecture a lower bound on the total number of binary bent sequences of a given order. This lower bound is exact for bent sequences of order 16; a list is included from which all such sequences can be derived. >

[1]  P. Vijay Kumar,et al.  Bounds on the linear span of bent sequences , 1983, IEEE Trans. Inf. Theory.

[2]  P. Vijay Kumar,et al.  Generalized Bent Functions and Their Properties , 1985, J. Comb. Theory, Ser. A.

[3]  Pavan Kumar,et al.  A new general construction for generalized bent functions , 1989, IEEE Trans. Inf. Theory.

[4]  Robert L. McFarland,et al.  A Family of Difference Sets in Non-cyclic Groups , 1973, J. Comb. Theory A.

[5]  Abraham Lempel,et al.  Maximal families of bent sequences , 1982, IEEE Trans. Inf. Theory.

[6]  R. Yarlagadda,et al.  A note on the eigenvectors of Hadamard matrices of order 2n , 1982 .

[7]  R. Yarlagadda,et al.  Analysis and synthesis of bent sequences , 1989 .

[8]  O. S. Rothaus,et al.  On "Bent" Functions , 1976, J. Comb. Theory, Ser. A.

[9]  Willi Meier,et al.  Nonlinearity Criteria for Cryptographic Functions , 1990, EUROCRYPT.

[10]  Robert A. Scholtz,et al.  Bent-function sequences , 1982, IEEE Trans. Inf. Theory.