论文信息 - Bent Functions, Partial Difference Sets, and Quasi-Frobenius Local Rings

Bent Functions, Partial Difference Sets, and Quasi-Frobenius Local Rings

Bent functions andpartial difference sets have been constructed from finite principalideal local rings. In this paper, the constructions are generalizedto finite quasi-Frobenius local rings. Let R bea finite quasi-Frobenius local ring with maximal ideal M.Bent functions and certain partial difference sets on M } M are extended to R } R.

Xiang-dong Hou | Xiang-dong Hou

[1] J. Dillon. Elementary Hadamard Difference Sets , 1974 .

[2] Siu Lun Ma,et al. A survey of partial difference sets , 1994, Des. Codes Cryptogr..

[3] Hans Dobbertin,et al. Construction of Bent Functions and Balanced Boolean Functions with High Nonlinearity , 1994, FSE.

[4] Philippe Langevin. On Generalized Bent Functions , 1993 .

[5] Siu Lun Ma,et al. Constructions of Partial Difference Sets and Relative Difference Sets on p-Groups , 1990 .

[6] Xiang-dong Hou. q-ary Bent Functions Constructed from Chain Rings , 1998 .

[7] Qing Xiang,et al. Constructions of Partial Difference Sets and Relative Difference Sets Using Galois Rings II , 1996, J. Comb. Theory, Ser. A.

[8] Claude Carlet,et al. A Characterization of Binary Bent Functions , 1996, J. Comb. Theory, Ser. A.

[9] Siu Lun Ma,et al. Partial Difference Sets with Paley Parameters , 1995 .

[10] B. R. McDonald. Finite Rings With Identity , 1974 .

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

[12] Philippe Langevin,et al. Results on Bent Functions , 1997, J. Comb. Theory, Ser. A.

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