The existence of (q,k,?,t)-ADFs(q,k,?,t)-ADFs for k=4,5,6?

Abstract Almost difference families ( ( q , k , λ , t ) -ADFs ) were introduced by Ding and Yin as an useful generalization of almost difference sets (ADSs), constructions and infinite classes of almost difference families were also presented. In this paper, several new infinite classes of ( q , k , λ , t ) -ADFs for k=4, 5 and 6 are constructed.

[1]  X. Wang,et al.  The existence of almost difference families , 2009 .

[2]  Yuan Zhang,et al.  A new family of almost difference sets and some necessary conditions , 2006, IEEE Trans. Inf. Theory.

[3]  Douglas R Stinson,et al.  Surveys in Combinatorics, 1999: Applications of Combinatorial Designs to Communications, Cryptography, and Networking , 1999 .

[4]  T. Storer Cyclotomy and difference sets , 1967 .

[5]  Jianxing Yin,et al.  Some combinatorial constructions for optical orthogonal codes , 1998, Discret. Math..

[6]  Charles J. Colbourn,et al.  Cyclic Block Designs With Block Size 3 , 1981, Eur. J. Comb..

[7]  Cunsheng Ding,et al.  Autocorrelation Values of Generalized Cyclotomic Sequences of Order Two , 1998, IEEE Trans. Inf. Theory.

[8]  Cunsheng Ding,et al.  Constructions of almost difference families , 2008, Discret. Math..

[9]  Cunsheng Ding,et al.  Highly nonlinear mappings , 2004, J. Complex..

[10]  Fan Chung Graham,et al.  Optical orthogonal codes: Design, analysis, and applications , 1989, IEEE Trans. Inf. Theory.

[11]  James A. Davis Almost difference sets and reversible divisible difference sets , 1992 .

[12]  Abraham Lempel,et al.  A class of balanced binary sequences with optimal autocorrelation properties , 1977, IEEE Trans. Inf. Theory.

[13]  Arne Winterhof,et al.  Some notes on the two-prime generator of order 2 , 2005, IEEE Transactions on Information Theory.

[14]  Cunsheng Ding,et al.  Almost difference sets and their sequences with optimal autocorrelation , 2001, IEEE Trans. Inf. Theory.