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: | Article |
| Language: | English |
| Published: |
2009
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| Online Access: | https://hdl.handle.net/10356/91551 http://hdl.handle.net/10220/6041 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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