论文信息 - Optimal and perfect difference systems of sets

Optimal and perfect difference systems of sets

Difference systems of sets (DSS) were introduced in 1971 by Levenstein for the construction of codes for synchronization, and are closely related to cyclic difference families. In this paper, algebraic constructions of difference systems of sets using functions with optimum nonlinearity are presented. All the difference systems of sets constructed in this paper are perfect and optimal. One conjecture on difference systems of sets is also presented.

Cunsheng Ding | C. Ding

[1] Vladimir D. Tonchev,et al. Optimal Difference Systems of Sets with Multipliers , 2006, CSR.

[2] Tor Helleseth,et al. A New Family of Ternary Sequences with Ideal Two-level Autocorrelation Function , 2001, Des. Codes Cryptogr..

[3] Vladimir D. Tonchev,et al. An algorithm for optimal difference systems of sets , 2007, J. Comb. Optim..

[4] Rudolf Lide,et al. Finite fields , 1983 .

[5] Vladimir D. Tonchev,et al. Hyperplane partitions and difference systems of sets , 2006, J. Comb. Theory A.

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

[7] T. Helleseth,et al. A New Family of Ternary Sequences with Ideal Two-level Autocorrelation Function , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[8] V. Levenshtein. Combinatorial problems motivated by comma‐free codes , 2004 .

[9] Cunsheng Ding,et al. Complex Codebooks From Combinatorial Designs , 2006, IEEE Transactions on Information Theory.

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

[11] Vladimir D. Tonchev,et al. Partitions of difference sets and code synchronization , 2005, Finite Fields Their Appl..