On (p^a,p^b,p^a,p^{a-b})-relative difference sets
This paper provides new exponent and rank conditions for the existence of abelian relative (p^a,p^b,p^a,p^a-b) -difference sets. It is also shown that no splitting relative (2^2c,2^d,2^2c,2^2c-d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (...
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sg-ntu-dr.10356-915512023-02-28T19:37:38Z On (p^a,p^b,p^a,p^{a-b})-relative difference sets Schmidt, Bernhard School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics This paper provides new exponent and rank conditions for the existence of abelian relative (p^a,p^b,p^a,p^a-b) -difference sets. It is also shown that no splitting relative (2^2c,2^d,2^2c,2^2c-d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group G\not\cong Z_8\times Z_4\times Z_2 exists if and only if \exp(G)\le 4 or G= Z_8\times ( Z_2)^3 with N\cong Z_2\times Z_2. Accepted version 2009-08-11T07:42:44Z 2019-12-06T18:07:44Z 2009-08-11T07:42:44Z 2019-12-06T18:07:44Z 1996 1996 Journal Article Schmidt, B. (1996). On (p^a,p^b,p^a,p^{a-b})-relative difference sets. Journal of algebraic combinatorics, 6(3), 279-297. 0925-9899 https://hdl.handle.net/10356/91551 http://hdl.handle.net/10220/6041 10.1023/A:1008674331764 en Journal of algebraic combinatorics. Journal of algebraic combinatorics © copyright 1997 Springer U.S. The journal's website is located at http://www.springerlink.com/content/l2u667032704718h. 23 p. application/pdf |
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DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics Schmidt, Bernhard On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| description |
This paper provides new exponent and rank conditions for the existence of abelian relative (p^a,p^b,p^a,p^a-b) -difference sets. It is also shown that no splitting relative (2^2c,2^d,2^2c,2^2c-d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group G\not\cong Z_8\times Z_4\times Z_2 exists if and only if \exp(G)\le 4 or G= Z_8\times ( Z_2)^3 with N\cong Z_2\times Z_2. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Schmidt, Bernhard |
| format |
Article |
| author |
Schmidt, Bernhard |
| author_sort |
Schmidt, Bernhard |
| title |
On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| title_short |
On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| title_full |
On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| title_fullStr |
On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| title_full_unstemmed |
On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| title_sort |
on (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| publishDate |
2009 |
| url |
https://hdl.handle.net/10356/91551 http://hdl.handle.net/10220/6041 |
| _version_ |
1759852991654920192 |