New Families of Semi-Regular Relative Difference Sets

被引：13

作者：

Davis J.A. ^{[1
]}

Jedwab J. ^{[2
]}

Mowbray M. ^{[2
]}

机构：

[1] Dept. of Math. and Computer Science, University of Richmond

[2] Hewlett-Packard Laboratories, Filton Road, Stoke Gifford

来源：

Designs, Codes and Cryptography | 1998年 / 13卷 / 2期

关键词：

Character theory; Combinatorics; Difference set; Relative difference set;

D O I：

10.1023/A:1008222227987

中图分类号：

学科分类号：

摘要：

We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the first such RDSs, and for u = 2 we obtain new examples.

引用

页码：131 / 146

页数：15

共 12 条

[1]

Arasu, K.T., Davis, J.A., Jedwab, J., Sehgal, S.K., New constructions of Menon difference sets (1993) J. Combin. Theory (A), 64, pp. 329-336

[2]

Davis, J.A., Jedwab, J., A note on new semi-regular divisible difference sets (1993) Designs, Codes and Cryptography, 3, pp. 373-381

[3]

Davis, J.A., Jedwab, J., Nested Hadamard difference sets (1997) J. Stat. Planning Inf., 62, pp. 13-20

[4]

Davis, J.A., Jedwab, J., A unifying construction for difference sets J. Combin. Theory (A), , To appear

[5]

Ganley, M.J., Direct product difference sets (1977) J. Combin. Theory (A), 23, pp. 321-332

[6]

Jungnickel, D., On automorphism groups of divisible designs (1982) Canad. J. Math., 34, pp. 257-297

[7]

Jungnickel, D., (1992) Difference Sets, Contemporary Design Theory: A Collection of Surveys, pp. 241-324. , (J. H. Dinitz and D. R. Stinson, eds.), Wiley, New York

[8]

Lander, E.S., (1983) Symmetric Designs: An Algebraic Approach, London Mathematical Society Lecture Notes Series 74, , Cambridge University Press, Cambridge

[9]

Ma, S.L., Schmidt, B., On (pa, p, pa, pa-1)-relative difference sets (1995) Designs, Codes and Cryptography, 6, pp. 57-71

[10]

Pott, A., (1995) Finite Geometry and Character Theory, , Lecture Notes in Mathematics 1601, Springer-Verlag, Berlin

← 1 2 →