论文信息 - Pairwise balanced designs from finite fields

Pairwise balanced designs from finite fields

Abstract Developing previous work by R.C. Bose, R.M. Wilson, M. Greig and the author, we give a general construction for difference families over finite fields. All the DFs constructed before were generated by a single initial base block so that they were uniform. Here we also consider DFs generated by two or more initial base blocks. These DFs give rise to pairwise balanced designs which of course are balanced block designs exactly when the initial base blocks have constant size.

Marco Buratti | M. Buratti

[1] Steven Furino,et al. Difference families from rings , 1991, Discret. Math..

[2] Hanfried Lenz,et al. Design theory , 1985 .

[3] Richard M. Wilson,et al. Cyclotomy and difference families in elementary abelian groups , 1972 .

[4] Dieter Jungnickel,et al. On the existence of small quasimultiples of affine and projective planes of arbitrary order , 1990, Discret. Math..

[5] E. Netto. Zur Theorie der Tripelsysteme , 1893 .

[6] R. Julian R. Abel. Forty-Three Balanced Incomplete Block Designs , 1994, J. Comb. Theory, Ser. A.

[7] R. C. Bose. ON THE CONSTRUCTION OF BALANCED INCOMPLETE BLOCK DESIGNS , 1939 .

[8] M. Buratti. On simple radical difference families , 1995 .

[9] Marco Buratti. A packing problem its application to Bose's families , 1996 .

[10] Marco Buratti,et al. A powerful method for constructing difference families and optimal optical orthogonal codes , 1995, Des. Codes Cryptogr..

[11] Malcolm Greig. Recursive Constructions of Balanced Incomplete Block Designs with Block Size of 7 , 2001, Ars Comb..

[12] Marco Buratti,et al. Constructions of (q, k, 1) difference families with q a prime power and k = 4, 5 , 1995, Discret. Math..

[13] R.J.R. Abel. Some new BIBDS with ? = 1 and 6 ?k ? 10 , 1996 .

[14] M. Buratti. Improving two theorems of bose on difference families , 1995 .