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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| Format: | Journal Article |
| Language: | English |
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2009
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| Online Access: | https://hdl.handle.net/10356/91551 http://hdl.handle.net/10220/6041 |
| _version_ | 1826109769275932672 |
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| author | Schmidt, Bernhard |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Schmidt, Bernhard |
| author_sort | Schmidt, Bernhard |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T02:23:41Z |
| format | Journal Article |
| id | ntu-10356/91551 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:23:41Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | ntu-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 |
| spellingShingle | DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics Schmidt, Bernhard On (p^a,p^b,p^a,p^{a-b})-relative difference sets |
| title | 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_short | 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 |
| topic | DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics |
| url | https://hdl.handle.net/10356/91551 http://hdl.handle.net/10220/6041 |
| work_keys_str_mv | AT schmidtbernhard onpapbpapabrelativedifferencesets |