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Further progress on difference families with block size 4 or 5.
- Source :
- Designs, Codes & Cryptography; Jul2010, Vol. 56 Issue 1, p1-20, 20p, 2 Diagrams, 5 Charts
- Publication Year :
- 2010
-
Abstract
- A strong indication about the existence of a (7 p, 4, 1) difference family with p ≡ 7 (mod 12) a prime has been given in [11]. Here, developing some ideas of that paper, we give, much more generally, a strong indication about the existence of a cyclic ( pq, 4, 1) difference family whenever p and q are primes congruent to 7 (mod 12) and of a cyclic ( pq, 5, 1) difference family whenever p and q are primes congruent to 11 (mod 20). Indeed we give an algorithm for their construction that seems to be always successful and we have checked it works whenever both primes p and q do not exceed 1,000. All our ( pq, 4, 1) and ( pq, 5, 1) difference families have the nice property of admitting a multiplier of order 3 or 5, respectively, that fixes almost all base blocks. As an intermediate result we also find an optimal ( p, 5, 1) optical orthogonal code for every prime p ≡ 11 (mod 20) not exceeding 10,000. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09251022
- Volume :
- 56
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Designs, Codes & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 50244693
- Full Text :
- https://doi.org/10.1007/s10623-009-9335-6