A class of functions and their application in constructing semi-biplanes and association schemes

Discrete Mathematics

Volumn 202, Issue 1-3, 1999, Pages 21-31

  Coulter, Robert S ^a   Henderson, Marie ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Association scheme; Incidence geometry; Semi biplane

Indexed keywords

EID: 0037734834     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(98)00345-8     Document Type: Article

References (16)

1. T. Beth, C. Ding, On almost perfect nonlinear permutations, in: T. Helleseth (Ed.), Advances in Cryptology - Eurocrypt '93, Lecture Notes in Computer Science, vol. 765, Springer, Berlin, 1993, pp. 65-76.
2. C.J. Colbourn, J.H. Dinitz (Eds.), CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, FL, 1996.
3. R.S. Coulter, R.W. Matthews, Planar functions and planes of Lenz-Barlotti class II, Des. Codes Cryptogr. 10 (1997) 167-184.
4. T.W. Cusick, Highly nonlinear power functions on finite fields, Unpublished manuscript.
5. 2, Math. Z. 103 (1968) 239-258.
6. H. Dobbertin, Construction of bent functions and balanced boolean functions with high nonlinearity, Preprint.
7. A. Del Fra, On two new classes of semibiplanes, Discrete Math. 174 (1997) 107-116.
8. T. Helleseth, D. Sandberg, Some power mappings with low differential uniformity, Appl. Algebra Engrg. Comm. Comput. 8 (1997) 363-370.
9. D. Hughes, Biplanes and semi-biplanes, in: D.A. Holton, J. Seberry (Eds.), Combinatorial Mathematics, Lecture Notes in Mathematics, vol. 686, Springer, Berlin, 1978, pp. 55-58.
10. T. Kasami, The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes, Inform. and Control 18 (1971) 369-394.
11. R. Lidl, H. Niederreiter, Finite Fields, Encyclopedia Math. Appl., vol. 20, Addison-Wesley, Reading, MA, 1983 (now distributed by Cambridge University Press).
12. K. Nyberg, Differentially uniform mappings in cryptography, in: T. Helleseth (Ed.), Advances in Cryptology - Eurocrypt '93, Lecture Notes in Computer Science, vol. 765, Springer, Berlin, 1993, pp. 55-64.
13. K. Nyberg, L.R. Knudsen, Provable security against differential cryptanalysis, in: E.F. Brickell (Ed.), Advances in Cryptology - Crypto '92 Lecture Notes in Computer Science, vol. 740, Springer, Berlin, 1992, pp. 566-574.
14. L. Rónyai, T. Szonyi, Planar functions over finite fields, Combinatorica 9 (1989) 315-320.
15. P. Wild, Generalized Hussain graphs and semibiplanes, Ars Combin. 14 (1982) 147-167.
16. P. Wild, Some families of semibiplanes, Discrete Math. 138 (1995) 397-403.